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Journal articles on the topic 'Simple random sampling without Replacement'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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1

Vincent, Odhiambo, Hellen Waititu, and Nyakundi Omwando Cornelious. "Nonparametric Estimation of Error Variance under Simple Random Sampling without Replacement." International Journal of Mathematics And Computer Research 10, no. 10 (2022): 2925–33. http://dx.doi.org/10.47191/ijmcr/v10i10.02.

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This study adopts a nonparametric approach in the estimation of a finite population error variance in the setting where the variance is a constant (homoscedastic) using a model-based technique under simple random sampling without replacement (SRSWOR). A mean square analysis of the estimator has been conducted, including the asymptotic behaviour of the estimator and the results show that the asymptotic distribution in a homoscedastic setting is asymptotically unbiased and consistent. The performance of the developed estimator is compared to that of other existing estimators using real data. R statistical software was utilized to analyze data and numerical results presented graphically for selected models.

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2

Milbrodt, Hartmut. "An invariance principle forU-statistics in simple random sampling without replacement." Metrika 34, no. 1 (1987): 195–200. http://dx.doi.org/10.1007/bf02613149.

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3

Odhiambo, Vincent, Waititu Hellen, and Omwando Cornelious Nyakundi. "NONPARAMETRIC ESTIMATION OF ERROR VARIANCE UNDER SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 10 (2022): 2925–33. https://doi.org/10.5281/zenodo.7229084.

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This study adopts a nonparametric approach in the estimation of a finite population error variance in the setting where the variance is a constant (homoscedastic) using a model-based technique under simple random sampling without replacement (SRSWOR). A mean square analysis of the  estimator has been conducted, including the asymptotic behaviour of the  estimator and the results show that the asymptotic distribution in a homoscedastic setting is asymptotically unbiased and consistent. The performance of the developed estimator is compared to that of other existing estimators using real data. R statistical software was utilized to analyze data and numerical results presented graphically for selected models.       

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4

Joarder, Anwar H., and A. M. Mujahidul Islam. "Inclusion Probability in Simple Random Sampling by Hypergeometric Distribution." BL College Journal 4, no. 2 (2022): 73–89. http://dx.doi.org/10.62106/blc2022v4i2e1.

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We review important probability issues in sampling from simple random sampling without replacement. The inclusion probability can be calculated by enumerating samples which is formidable for most cases of large samples or large population. A good number of possible situations have been considered. We prove that hypergeometric mass function provides an elegant solution to the problem.

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5

Kumar Adichwal, Nitesh, Abdullah Ali H. Ahmadini, Yashpal Singh Raghav, Rajesh Singh, and Irfan Ali. "Estimation of general parameters using auxiliary information in simple random sampling without replacement." Journal of King Saud University - Science 34, no. 2 (2022): 101754. http://dx.doi.org/10.1016/j.jksus.2021.101754.

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6

Singh, Poonam, and Rajesh Singh. "Improved generalized exponential estimators in simple random sampling without replacement using some transformations." Journal of Statistics and Management Systems 27, no. 7 (2024): 1413–31. https://doi.org/10.47974/jsms-1224.

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This article suggests three generalized exponential estimators using an auxiliary variable for estimating population mean with some transformations. The mean squared error expressions are derived up to the first order approximation for comparing the efficiency of the proposed estimators with the existing estimators in literature. We compared the efficiency of the proposed estimators with the usual mean estimator, [2] ratio estimator, [1] ratio type exponential estimator, [15] and [9] usual regression estimator. It is found that our proposed estimators perform better than these existing estimators in the literature. Findings are empirically verified using three real data sets and a simulation study.

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7

Marshall, P. L. "A Microcomputer Program for Assisting in the Design of Simple Random Samples." Forestry Chronicle 63, no. 6 (1987): 422–25. http://dx.doi.org/10.5558/tfc63422-6.

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An interactive microcomputer program was developed to aid the design of simple random sampling with or without replacement. The program determines: (1) sample size for a set of given conditions for up to 20 variables; (2) combinations of conditions that will yield a given samples size; and (3) the relationship between percentage error and sample size for a given set of conditions. Potential applications are illustrated with three simple examples. Key Words: sample size, simple random sampling

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8

Chadyšas, Viktoras, and Danutė Krapavickaitė. "Estimation of the current population total for a four-phase sampling design." Nonlinear Analysis: Modelling and Control 21, no. 2 (2016): 241–60. http://dx.doi.org/10.15388/na.2016.2.7.

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The combined ratio-type estimators of the finite population total and their variances in the case of sample rotation for two-phase and four-phase sampling schemes are constructed in the paper. Combined estimators of the finite population total without and with the use of auxiliary information known from the previous survey are built. Two types of sampling design are used for sample selection in each of the phases: simple random sampling without replacement and successive sampling without replacement with probabilities proportional to size. A simulation study, based on the real data, is performed, and the accuracy of the estimators proposed is compared.

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9

Wywiał, Janusz. "Estimation of mean on the basis of conditional simple random sample." Statistics in Transition new series 17, no. 3 (2016): 411–28. http://dx.doi.org/10.59170/stattrans-2016-024.

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Estimation of the population mean in a finite and fixed population on the basis of the conditional simple random sampling design dependent on order statistics (quantiles) of an auxiliary variable is considered. Properties of the well-known Horvitz-Thompson and ratio type estimators as well as the sample mean are taken into account under the conditional simple random sampling designs. The considered examples of empirical analysis lead to the conclusion that under some additional conditions the proposed estimation strategies based on the conditional simple random sample are usually more accurate than the mean from the simple random sample drawn without replacement.

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10

Makumi, Nicholas, Romanus Odhiambo Otieno, George Otieno Orwa, Festus Were, and Habineza Alexis. "Bias Correction Technique for Estimating Quantiles of Finite Populations under Simple Random Sampling without Replacement." Open Journal of Statistics 11, no. 05 (2021): 854–69. http://dx.doi.org/10.4236/ojs.2021.115050.

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11

Ahmed, M. S., and Atsu S. S. Dorvlo. "A GENERAL CLASS OF ESTIMATORS UNDER MULTI PHASE SAMPLING." Statistics in Transition new series 10, no. 2 (2009): 183–92. http://dx.doi.org/10.59170/stattrans-2009-015.

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This paper derives the general estimators for finite population mean using multivariate auxiliary information under multiphase sampling. Here a number of auxiliary variables are considered in each phase under general sampling design. The properties of these estimators are studied and the results are presented for simple random sampling without replacement (SRSWOR) scheme. Using a modified cost function the optimum sample sizes are also derived.

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12

Mukhopadhyay, N., and S. Chattopadhyay. "Simultaneous Estimation of Proportions in a Finite Population." Calcutta Statistical Association Bulletin 43, no. 1-2 (1993): 65–74. http://dx.doi.org/10.1177/0008068319930106.

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Sequential and multistage sampling strategies via simple random sampling without replacement, are proposed for simultaneously estimating several proportions in a finite population. Various asymptotic first-order properties are addressed, while some limited moderate sample performance have also been included. AMS (1980) Subject Classification: Primary 62L99; Secondary 62L12

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13

Aubry, Philippe. "On the implementation of stratified two-stage simple random sampling without replacement, with possible collapsed strata." MethodsX 13 (December 2024): 102928. http://dx.doi.org/10.1016/j.mex.2024.102928.

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14

Ounrittichai, Nuntida, Patsaporn Utha, Boonyarit Choopradit, and Saowapa Chaipitak. "Performance Comparison of Three Ratio Estimators of the Population Ratio in Simple Random Sampling Without Replacement." International Journal of Analysis and Applications 22 (July 29, 2024): 121. http://dx.doi.org/10.28924/2291-8639-22-2024-121.

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This study aims to compare the efficacy of three ratio estimators for estimating the population ratio in simple random sampling without replacement (SRSWOR). The estimators under consideration are a customary ratio estimator (~R1), a ratio estimator based on a transformed mean estimator (~R2) introduced by Onyeka et al. [1], and a regression-type estimator (~R3) proposed by Onyeka et al. [2]. We assess the performance of these estimators across three distributions (bivariate normal, bivariate Poisson log-normal, and bivariate Cauchy) while varying both correlation coefficients and sample sizes, utilizing Mean Square Error (MSE) and Percent Relative Efficiency (PRE) as evaluation criteria. The results indicate that for a bivariate normal distribution, the ~R1 and ~R2 estimators consistently outperformed the ~R3 estimator across all sample sizes and correlation coefficients. The ~R2 estimator demonstrated superiority with very small sample sizes, while ~R1 exhibited better performance in small sample sizes. The ~R2 estimator remained reliable for moderately sized samples, demonstrating consistent efficiency. In large samples, ~R2 maintained its performance advantage, except in weak correlation coefficients, where ~R1 proved superior. For a bivariate Poisson lognormal distribution, both ~R2 and ~R3 performed significantly better than ~R1 for very small sample sizes, irrespective of correlation direction and strength. For moderately sized samples, ~R2 and ~R3 consistently excelled, with ~R2 leading in cases with positive correlation coefficients. For large sample sizes with negative correlation coefficients, both ~R2 and ~R3 were comparable effective and significantly better than ~R1. Conversely, with positive correlation coefficients, the ~R1 estimator significantly outperformed both ~R2 and ~R3. In a bivariate Cauchy distribution, the ~R1 estimator demonstrated notable and consistent superiority over the ~R2 and ~R3 estimators across all sample sizes and correlation coefficients.

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15

Chaudhuri, Arijit, and Sonakhya Samaddar. "Estimating the population mean using a complex sampling design dependent on an auxiliary variable." Statistics in Transition New Series 23, no. 1 (2022): 39–54. http://dx.doi.org/10.2478/stattrans-2022-0003.

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Abstract In surveying finite populations, the simplest strategy to estimate a population total without bias is to employ Simple Random Sampling (SRS) with replacement (SRSWR) and the expansion estimator based on it. Anything other than that including SRS Without Replacement (SRSWOR) and usage of the expansion estimator is a complex strategy. We examine here (1) if from a complex sample at hand a gain in efficiency may be unbiasedly estimated comparing the “rival population total-estimators” for the competing strategies and (2) how suitable model-expected variances of rival estimators compete in magnitude as examined numerically through simulations.

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16

Antonijević, Marija, and Đina Ivanović. "Evaluation of the human development index (HDI) using the methods of sample theory." International Journal of Economic Practice and Policy 18, no. 1 (2021): 14–32. http://dx.doi.org/10.5937/skolbiz1-28866.

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This paper aims to determine which of the two sample plans, i.e., a simple random sample without replacement, or a stratified sample, gives a more accurate estimate of the feature's mean. The feature that was the subject of this research is the human development index in 2018. The analysis included 189 countries globally, classified into specific categories according to the United Nations development classification. The research results showed that a more accurate estimate of the mean of the human development index was obtained by applying a stratified sampling since the mean of the human development index is close to the population mean. Also, the variance of the sample mean is lower than the value obtained by applying a simple random sampling without replacement. Therefore, it was justified to approach stratification, which indicates that in the case of conducting research, the use of a stratified sampling should be considered since it provides a more precise estimate of the mean.

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17

Pal, Sanghamitra. "Extending Takahasi‐Sakasegawa’s Indirect Response Technique to Cover Sensitive Surveys in Unequal Probability Sampling." Calcutta Statistical Association Bulletin 59, no. 3-4 (2007): 265–76. http://dx.doi.org/10.1177/0008068320070310.

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Abstract: Randomized Response (RR) Technique (RRT), introduced by Warner (1965), is a well‐known way to unbiasedly estimate proportions of people bearing sensitive characteristics. Takahasi and Sakasegawa (1977) narrated a novel procedure avoiding any particular RR device unlike most researchers in this field. Most RRT’s in the literature give estimators for population totals and variance estimators thereof, allowing exclusively simple random sampling with replacement (SRSWR) schemes, including as well the above too. We present formulae applicable to general varying probability sampling, even without replacement applying Takahasi‐ Sakasegawa device. AMS (2000) Subject Classification: 62D05.

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18

Carlson, Colleen A., Thomas R. Fox, Harold E. Burkhart, H. Lee Allen, and Timothy J. Albaugh. "Accuracy of Subsampling for Height Measurements in Loblolly Pine Plots." Southern Journal of Applied Forestry 33, no. 3 (2009): 145–49. http://dx.doi.org/10.1093/sjaf/33.3.145.

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Abstract Estimating heights in research and inventory plots is costly. We examined the feasibility of subsampling tree heights as opposed to measuring all trees. Four sampling intensities (75, 50, 25, and 10%) and four sampling strategies (systematic sampling, simple random sampling without replacement, stratified sampling across the diameter distribution, and sampling the first trees in each plot) were investigated. Data from 600 loblolly pine plots in fertilizer trials in the southeastern United States were used. The application of a height–dbh regression to predict the heights of unmeasured trees was also investigated. Sampling the first trees generally resulted in poorer estimates than the other sampling schemes. Systematic and simple random sampling performed similarly. A 50% sampling intensity with either systematic or simple random sampling and a height–dbh regression predicting the heights of unmeasured trees estimated more than 90% of plots to within 2.2% of the observed plot height and more than 94% of plots to within 2.5% of the observed volume, and they were more accurate than the stratified sampling at the same intensity. Systematic sampling is easy to implement, requiring no prior plot knowledge. We conclude that a 50% systematic sampling combined with a height–dbh regression will reduce costs without compromising accuracy.

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19

Arabatzis, Alexandros A., and Harold E. Burkhart. "An Evaluation of Sampling Methods and Model Forms for Estimating Height-Diameter Relationships in Loblolly Pine Plantations." Forest Science 38, no. 1 (1992): 192–98. http://dx.doi.org/10.1093/forestscience/38.1.192.

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Abstract The prediction performance of eight height-diameter regression models was compared for estimating mean stand height when fitted to data selected from 175 loblolly pine (Pinus taeda) sample plots by (i) simple random sampling without replacement, and (ii) stratified random sampling with dbh classes acting as strata. Among the models tested, the nonlinear model of the form H = aeb/D performed best especially when fitted to data selected by simple random sampling. A small gain in precision obtained by stratification into dbh classes was outweighed by a substantial increase in bias due to the arbitrary allocation of numbers of sample trees to the strata. To update existing height-diameter models, it is recommended that new trees be selected and measured on every occasion instead of retaining the same sample trees used previously for model fitting. For. Sci. 38(1):192-198.

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20

Chutiman, Nipaporn, Athipakon Nathomthong, Supawadee Wichitchan, and Pannarat Guayjarernpanishk. "Improved Estimator Using Auxiliary Information in Adaptive Cluster Sampling with Networks Selected Without Replacement." Symmetry 17, no. 3 (2025): 375. https://doi.org/10.3390/sym17030375.

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Adaptive cluster sampling (ACS) is an efficient sampling technique for studying populations where the characteristic of interest is rare or spatially clustered. This method is widely applied in fields such as ecological studies, epidemiology, and resource management. ACS initially selects sampling units using simple random sampling without replacement. However, in some cases, selected networks may overlap, leading to multiple networks being included in the sample. To address this issue, a modified version of ACS was developed to ensure sampling without replacement at the network level, maintaining sampling symmetry and preventing the inclusion of overlapping networks. Despite this adjustment, asymmetry may still occur when network formation is highly irregular. This issue can be mitigated by incorporating auxiliary variables, which help correct distortions in the sampling process. In many situations, auxiliary variables related to the variable of interest can be utilized to enhance the precision of population parameter estimates. This research proposes multiplicative generalization for an estimator with two auxiliary variables using adaptive cluster sampling with networks selected without replacement. The bias and mean square error (MSE) are derived using a Taylor series expansion to determine the optimal conditions for minimizing MSE. A simulation study is conducted to support the theoretical findings. The results show that the proposed estimator under the optimal values of T1 and T2 is the most efficient to minimize MSE.

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21

Onyeka, A. C. "A class of product-type exponential estimators of the population mean in simple random sampling scheme." Statistics in Transition new series 14, no. 2 (2013): 189–200. http://dx.doi.org/10.59170/stattrans-2013-012.

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The present study proposes a class of product-type exponential estimators for estimating the population mean of the study variable, using known values of some population parameters of an auxiliary character, under the simple random sampling without replacement (SRSWOR) scheme. Furthermore, the study also proposes a modified exponential estimator based on both the ratio-type and the product-type exponential estimators. Properties of the proposed estimators, under the SRSWOR scheme, are obtained up to first order approximation. The modified exponential estimator under optimum conditions is shown to be more efficient than the simple sample mean and the ratio-type and product-type exponential estimators. The theoretical results are supported by an empirical illustration.

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22

Sinha, Bikas K., and S. Sengupta. "Estimation of the Probability of Discovering a New Category in Finite Population Sampling." Calcutta Statistical Association Bulletin 43, no. 1-2 (1993): 75–84. http://dx.doi.org/10.1177/0008068319930107.

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Considered is the set-up of sampling from a finite population of N (known) units divided into k (unknown) mutually exclusive and exhaustive categories, the ith category possessing N i, (unknown) units, 1 ⩽ i ⩽ k As and when sampling is terminated, some categories may remain undiscovered. A quantity of interest is the probability of discovering a new category when an additional draw is made. We address the problem of estimation of this unknown probability and also that of more general parametric functions. Simple random sampling (with/without replacement) is discussed.

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23

Isah, Muhammad Yahaya Zakari Mannir Abdu Rufai Iliyasu Mujtaba Suleiman Samaila Manzo Ali Muhammad and Adamu Zakar Adamu. "Enhanced Ratio-Type Estimator for Finite Population Mean using Auxiliary Variable in Simple Random Sampling." NIPES Journal of Science and Technology Research 5, no. 1 (2023): 242–52. https://doi.org/10.5281/zenodo.7745091.

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<em>In this paper, a ratio-type estimator of finite population mean in simple random sampling without replacement by using information on an auxiliary variable has been proposed. The proposed estimator was obtained by using the strategy of power transformation and incorporated the unknown weight (</em><em>). The objective of this study is to develop a new ratio estimator that provide better precision of estimation of population mean. The properties such as bias and mean square error (MSE) of the proposed estimator are derived and tested using four real data sets. The results of the empirical study revealed that the proposed ratio type estimator performed better than the existing estimators considered in the study. Therefore, the proposed estimator is more efficient than the existing estimators based on the criteria of mean square error and percent relative efficiency.</em>

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24

ZAMAN, TOLGA, SOOFIA IFTIKHAR, CAGLAR SOZEN, and PRAYAS SHARMA. "A NEW LOGARITHMIC TYPE ESTIMATORS FOR ANALYSIS OF NUMBER OF AFTERSHOCKS USING POISSON DISTRIBUTION." Journal of Science and Arts 24, no. 4 (2024): 833–42. https://doi.org/10.46939/j.sci.arts-24.4-a06.

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Earthquake is a fierce and unavoidable natural disaster. The study of aftershocks following an earthquake provides a comprehensive understanding of seismic activity, making it an important area of research. Although it is important to mention that the use of the Poisson distributed population, to estimate the mass mean of rare events such as earthquakes, has been little studied in the literature. In this context, this study proposes a new class of logarithmic type ratio estimators for estimating the mean of a Poisson distributed population in a simple random sampling without replacement. The proposed estimators are obtained using the logarithmic transformation of the ratio estimator, and the expressions for the mean square error (MSE) are also derived to the first order of approximation. The study demonstrates that the proposed logarithmic type estimators are more efficient than the existing estimators, both theoretically and empirically. The Empirical evidence from a real data study conducted using earthquake data from Turkey confirms the superiority of the proposed estimators over the existing estimators. The study provides valuable insights for researchers and practitioners working with Poisson distributed populations and requiring ratio estimators using simple random sampling without replacement.

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25

Swain, A. K. P. C. "On classes of modified ratio type and regression-cum-ratio type estimators in sample surveys using two auxiliary variables." Statistics in Transition new series 13, no. 3 (2013): 473–94. http://dx.doi.org/10.59170/stattrans-2012-035.

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In this paper generalized classes of modified ratio type and regression-cum-ratio type estimators of the finite population mean of the study variable are suggested in the presence of two auxiliary variables in simple random sampling without replacement when the population means of the auxiliary variables are known in advance. Some special cases of the generalized estimators are compared with respect to their biases and efficiencies both theoretically and with the help of some natural populations.

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26

Athreya, K. B. "Coalescence in Critical and Subcritical Galton-Watson Branching Processes." Journal of Applied Probability 49, no. 3 (2012): 627–38. http://dx.doi.org/10.1239/jap/1346955322.

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In a Galton-Watson branching process that is not extinct by the nth generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation Xn a pairwise coalescence time. Similarly, let Yn denote the coalescence time for the whole population of the nth generation conditioned on the event that it is not extinct. In this paper the distributions of Xn and Yn, and their limit behaviors as n → ∞ are discussed for both the critical and subcritical cases.

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Athreya, K. B. "Coalescence in Critical and Subcritical Galton-Watson Branching Processes." Journal of Applied Probability 49, no. 03 (2012): 627–38. http://dx.doi.org/10.1017/s0021900200009426.

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In a Galton-Watson branching process that is not extinct by the nth generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation X n a pairwise coalescence time. Similarly, let Y n denote the coalescence time for the whole population of the nth generation conditioned on the event that it is not extinct. In this paper the distributions of X n and Y n , and their limit behaviors as n → ∞ are discussed for both the critical and subcritical cases.

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28

IJAZ, MUHAMMAD, TOLGA ZAMAN, BUSHRA HAIDER, and SYED MUHAMMAD ASIM. "AN EFFICIENT CLASS OF PRODUCT ESTIMATORS USING MEASURES OF DISPERSIONS." Journal of Science and Arts 21, no. 2 (2021): 347–54. http://dx.doi.org/10.46939/j.sci.arts-21.2-a03.

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The study suggests a class of product estimators for estimating the population mean of variable under investigation in simple random sampling without replacement (SRSWOR) scheme when secondary information on standard deviation, mean deviation, and quartile deviation is available. The expression for Bias and Mean Square Error (MSE) has been derived. A comparison is made both theoretically and numerically with other existing product estimators. It is concluded that compared to other product type estimators, suggested class of estimators estimate the population mean more efficiently.

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29

Saha, Amitava. "On the Application of the Mirror‐Match Bootstrap in Adaptive Cluster Sampling." Calcutta Statistical Association Bulletin 59, no. 3-4 (2007): 223–38. http://dx.doi.org/10.1177/0008068320070307.

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Abstract: The confidence intervals (CT’s) conventionally constructed in large‐scale sample surveys assuming asymptotic normality often leads to unsatisfactory results when the population under study is rare or clustered. Adaptive cluster sampling is a promising sampling technique to effectively catch rare, geographically clustered or localized population elements. Christman and Pontius (2000) applied several bootstrap techniques to construct confidence intervals when simple random samples are selected without replacement (SRSWOR) and adaptive cluster sampling is used to sample localized population units. Here we extend Sitter's (1992a, b) ‘mirror‐match’ (MM) bootstrap to a practical survey set‐up using varying selection probability. We also demonstrate using real data from the Indian Economic Census how the extended procedure can be applied to adaptive cluster sampling adopted for estimating simultaneously the numbers of carners engaged in a number of localized unorganized rural industries. AMS (2000) Subject Classification: 62D05.

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30

Singh, Rajesh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan, and Florentin Smarandache. "A general family of dual to ratio-cum-product estimator in sample surveys." Statistics in Transition new series 12, no. 3 (2011): 587–94. http://dx.doi.org/10.59170/stattrans-2011-044.

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This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.

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31

Jambulingam, Subramani, and Ajith S. Master. "Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling." Nepalese Journal of Statistics 1 (December 29, 2017): 1–14. http://dx.doi.org/10.3126/njs.v1i0.18813.

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Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

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32

Zaman, Qamruz. "A Novel Class of Ratio Estimators Incorporating Auxiliary Variables in Simple Random Sampling for Estimating Population Mean: An Application to Real-Life Data." Power System Technology 48, no. 3 (2024): 609–21. http://dx.doi.org/10.52783/pst.851.

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This paper presents a novel class of ratio estimators using non-conventional measures as auxiliary information to estimate the population mean of the study variable under simple random sampling without replacement. Three special cases are discussed, utilizing the coefficient of variation, median, and quartile deviation as auxiliary variables. The bias and mean square error (MSE) of the proposed estimators are derived up to the first order of approximation. Furthermore, theoretical conditions are established to compare the proposed class with existing estimators, supported by real-life data. Numerical results demonstrate that the proposed class of estimators is more efficient than traditional and other ratio-type estimators.

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Mujib, Mujib, Mardiyah Mardiyah, and Suherman Suherman. "MODEL INTEGRATING SOCIETY, SCIENCE, ENVIRONMENT, TECHNOLOGY AND COLLABORATIVE MIND MAPPING MEMPENGARUHI PENALARAN MATEMATIS DAN MULTIPLE INTELLEGENCES." Jurnal Pendidikan Matematika Universitas Lampung 10, no. 1 (2022): 70–82. http://dx.doi.org/10.23960/mtk/v10i1.pp70-82.

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The reasoning is critical in all fields, but especially in mathematics. The purpose of this study is to ascertain the differences in students' mathematical reasoning abilities when they are exposed to learning that integrates society, science, the environment, technology, and collaborative mind mapping (ISSETCM2). This is a quasi-experiment with a population of 220 students and a sample size of 60 students. The sampling technique used is simple random sampling without replacement (without replacement). Mathematical reasoning tests based on essays and questionnaires assessing multiple intelligences. Validity, reliability, normality, homogeneity, and two-way ANOVA were used to analyze the data. The results indicated that while students' mathematical reasoning abilities improved when ISSETCM2 learning was used, there was no difference in students' mathematical reasoning abilities when conventional learning was used. Furthermore, there was no difference in students' mathematical reasoning abilities when multiple intelligences were classified as high, medium, or low. There is no interaction between learning methods and students' mathematical reasoning abilities at the high, medium, or low multiple intelligence levels.

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Mujib, Mujib, Mardiyah Mardiyah, Suherman Suherman, and Suherman Suherman. "MODEL INTEGRATING SOCIETY, SCIENCE, ENVIRONMENT, TECHNOLOGY AND COLLABORATIVE MIND MAPPING MEMPENGARUHI PENALARAN MATEMATIS DAN MULTIPLE INTELLEGENCES." At- Ta'lim : Jurnal Pendidikan 8, no. 1 (2022): 110–29. http://dx.doi.org/10.55210/attalim.v8i1.769.

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The reasoning is critical in all fields, but especially in mathematics. The purpose of this study is to ascertain the differences in students' mathematical reasoning abilities when they are exposed to learning that integrates society, science, the environment, technology, and collaborative mind mapping (ISSETCM2). This is a quasi-experiment with a population of 220 students and a sample size of 60 students. The sampling technique used is simple random sampling without replacement (without replacement). Mathematical reasoning tests based on essays and questionnaires assessing multiple intelligences. Validity, reliability, normality, homogeneity, and two-way ANOVA were used to analyze the data. The results indicated that while students' mathematical reasoning abilities improved when ISSETCM2 learning was used, there was no difference in students' mathematical reasoning abilities when conventional learning was used. Furthermore, there was no difference in students' mathematical reasoning abilities when multiple intelligences were classified as high, medium, or low. There is no interaction between learning methods and students' mathematical reasoning abilities at the high, medium, or low multiple intelligence levels.

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35

Singh, Housila P., Lakshmi N. Upadhyaya, and Premchandra. "AN IMPROVED VERSION OF REGRESSION RATIO ESTIMATOR WITH TWO AUXILIARY VARIABLES IN SAMPLE SURVEYS." Statistics in Transition new series 10, no. 1 (2009): 85–100. http://dx.doi.org/10.59170/stattrans-2009-006.

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This paper considers a family of estimators of population mean Y of the variable y under study using information on two auxiliary variables x and z under simple random sampling without replacement (SRSWOR) scheme. The expressions for bias and mean-squared error of the proposed family of estimators are obtained up to the first degree of approximation. In addition to many, Mohanty (1967), Khare and Srivastava (1981) and Upadhyaya and Singh (1984) estimators are identified as particular members of the suggested family. Asymptotic optimum estimator (AOE) in the family is identified with its approximate mean-squared error expression.

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Sinha, R. R., and Khanna Bharti. "Improved estimation of the mean through regressed exponential estimators based on sub-sampling non-respondents." Statistics in Transition new series 25, no. 3 (2024): 103–22. http://dx.doi.org/10.59170/stattrans-2024-030.

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The present study concerns the issue of estimating the population mean and presents novel and improved regressed exponential estimators using different parameters of an auxiliary character based on sub-sampling non-respondents. The bias and mean square error (MSE) of the proposed estimators for the most pragmatic simple random sampling without replacement (SRSWOR) scheme have been derived up to the first order of approximation (i.e. the expression containing errors up to the power of two so that the expectation comes only in terms of the mean, variance and covariance). The optimum value of the MSE of the estimators is found, along with the necessary conditions for optimising the MSE. The effectiveness of the suggested estimators, outperforming the existing ones in terms of their MSE, has been studied theoretically, while the empirical as well as the simulation studies have confirmed these findings.

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Mittal, Alisha, and Manoj Kumar. "Two new estimators of finite population variance under random non-response: An application." Model Assisted Statistics and Applications 18, no. 1 (2023): 73–84. http://dx.doi.org/10.3233/mas-221361.

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In this paper, an attempt has been made to study the estimation of finite population variance in simple random sampling without replacement (SRSWOR) in presence of non-response by proposing two estimators. The two estimators (dual to ratio and ratio cum dual to ratio type) have been proposed on the basis of availability and non-availability of auxiliary information. The properties such as bias and mean square error of the proposed estimators have also been studied up to first order of approximation. The proposed estimators are compared with some existing estimators and are also mutually compared. An empirical study, based on both vegetable crop data and simulated data, has been performed to find out the best estimator. It has been seen that out of the two proposed estimators, the ratio cum dual to ratio type estimator performed better than dual to ratio estimator.

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Hong, Zhi Min, and Zai Zai Yan. "A Unified Approach for Analysis of Randomized Response Surveys." Advanced Materials Research 143-144 (October 2010): 1259–63. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.1259.

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In this paper, we propose a class of estimators for the population mean of a sensitive variable, taking account into a generic randomization scheme, under the simple random sampling with replacement (SRSWR), when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also defined. We prove that the best estimator acts as a regression estimator which is at least as efficient as the corresponding estimator without the auxiliary variable. A new measure of privacy protection is built, and some models can be compared from the perspective of efficiency and privacy protection.

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Kumar, Sunil, and Monica Choudhary. "An Improved Estimator of finite Population Variance Using two Auxiliary Variable SRS." Revista Colombiana de Estadística 46, no. 1 (2023): 81–91. http://dx.doi.org/10.15446/rce.v46n1.104427.

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In the present study, we explore the problem of estimation of finite population variance in simple random sampling (without replacement) by utilizing information of two auxiliary variables. A ratio cum exponential estimator has been proposed and its properties are studied to the first degree of approximation. To demonstrate the efficiency, members of the proposed estimator as well as other existing estimators are compared to the usual unbiased estimator. To study the performance, a simulation study is undertaken for both real and artificial population using R software. The suggested estimator is found to be more efficient than other existing estimators in terms of having minimum MSE.

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Shukla, Diwakar, Sharad Pathak, and Narendra Singh Thakur. "Estimation of population mean using two auxiliary sources in sample surveys." Statistics in Transition new series 13, no. 1 (2013): 21–36. http://dx.doi.org/10.59170/stattrans-2012-002.

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This paper proposes families for estimation of population mean of the main variable under study using the information on two different auxiliary variables under simple random sampling without replacement (SRSWOR) scheme. Three different classes of estimators are constructed, examined with a complete study with other existing estimators. The expression for bias and mean squared error of the proposed families are obtained up to first order of approximation. Usual ratio estimator, product estimator, dual to ratio estimator, ratio-cum-product type estimator and many more estimators are identified as particular members of the suggested family. Expressions of optimization are derived and theoretical results are supported by numerical examples.

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Chaudhuri, Arijit. "Estimation from an Under-Covered Sample in a Complex Survey for Auditing." Calcutta Statistical Association Bulletin 54, no. 1-2 (2003): 115–20. http://dx.doi.org/10.1177/0008068320030110.

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We encounter a practical problem when from a finite population a complex survey design justifies selection of a sample in five stages. The design stipulates selecting a specified number of n(> 2) first stage units by Rao, Hartley and Cochran's (RHC, 1962) scheme followed by simple random sampling (SRS) without replacement (WOR) in each of the four subsequent stages. At the implementation stage a resource crunch calls for reducing the first stage sample size from n to m ( m < n). The consequential modifications in the methods of estimation of population total, mean and ratio of two totals and those of the variance of the first and the mean square errors of the latter two estimators are spelt out. The problem arises in the context of designing audits of Government documents by appropriate sampling.

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42

Antoch, Jaromír, Francesco Mola, and Ondřej Vozár. "New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable." Statistika: Statistics and Economy Journal 102, no. 2 (2022): 205–27. http://dx.doi.org/10.54694/stat.2022.11.

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A new randomized response technique for estimating the population total, or the population mean of a quantitative variable is proposed. It provides a high degree of protection to the respondents because they never report their data. Therefore, it may be favorably perceived by them and increase their willingness to cooperate. Instead of revealing the true value of the characteristic under investigation, the respondent only states whether the value is greater (or smaller) than a number which is selected by him/her at random and is unknown to the interviewer. For each respondent, this number, a sort of individual threshold, is generated as a pseudorandom number. Furthermore, two modifications of the proposed technique are presented. The first modification assumes that the interviewer also knows the generated random number. The second modification deals with the issue that, for certain variables, such as income, it may be embarrassing for the respondents to report either high or low values. Thus, depending on the value of the fixed threshold (unknown to the respondent), the respondent is asked different questions to avoid being embarrassed. The suggested approach is applied in detail to the simple random sampling without replacement, but it can be, after a straightforward modification, applied to many sampling schemes, including cluster sampling, two-stage sampling, or stratified sampling. The results of the simulations illustrate the behavior of the proposed technique.

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Hong, Jyy-I. "Coalescence in Subcritical Bellman-Harris Age-Dependent Branching Processes." Journal of Applied Probability 50, no. 2 (2013): 576–91. http://dx.doi.org/10.1239/jap/1371648962.

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We consider a continuous-time, single-type, age-dependent Bellman-Harris branching process. We investigate the limit distribution of the point process A(t)={at,i: 1≤ i≤ Z(t)}, where at,i is the age of the ith individual alive at time t, 1≤ i≤ Z(t), and Z(t) is the population size of individuals alive at time t. Also, if Z(t)≥ k, k≥2, is a positive integer, we pick k individuals from those who are alive at time t by simple random sampling without replacement and trace their lines of descent backward in time until they meet for the first time. Let Dk(t) be the coalescence time (the death time of the last common ancestor) of these k random chosen individuals. We study the distribution of Dk(t) and its limit distribution as t→∞.

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Irfan, Muhammad, Maria Javed, Sandile C. Shongwe, Muhammad Zohaib, and Sajjad Haider Bhatti. "Estimation of Population Median under Robust Measures of an Auxiliary Variable." Mathematical Problems in Engineering 2021 (September 16, 2021): 1–14. http://dx.doi.org/10.1155/2021/4839077.

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In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

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Hong, Jyy-I. "Coalescence in Subcritical Bellman-Harris Age-Dependent Branching Processes." Journal of Applied Probability 50, no. 02 (2013): 576–91. http://dx.doi.org/10.1017/s0021900200013577.

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We consider a continuous-time, single-type, age-dependent Bellman-Harris branching process. We investigate the limit distribution of the point process A(t)={a t,i : 1≤ i≤ Z(t)}, where a t,i is the age of the ith individual alive at time t, 1≤ i≤ Z(t), and Z(t) is the population size of individuals alive at time t. Also, if Z(t)≥ k, k≥2, is a positive integer, we pick k individuals from those who are alive at time t by simple random sampling without replacement and trace their lines of descent backward in time until they meet for the first time. Let D k(t) be the coalescence time (the death time of the last common ancestor) of these k random chosen individuals. We study the distribution of D k(t) and its limit distribution as t→∞.

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J. Moya Fernández, Pablo, Encarnación Álvarez, and Ángela González Medina. "An Analysis of the Impact of Various Sampling Designs on the Headcount Index: A Simulation Study Based on the EU-SILC." Journal of Social Sciences Research, no. 610 (October 31, 2020): 914–22. http://dx.doi.org/10.32861/jssr.610.914.922.

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The analysis and the comparison of poverty between regions and countries are important topics in social sciences, which have relevant demands of many national (Cáritas, Intermón Oxfam, Cruz Roja, etc) and international (UN, World Bank, OECD, Eurostat, IMF, etc) agencies and organizations. One of the most common poverty indicators in practice is the headcount index, which analyzes the proportion of individuals considered as poor in a population. In this paper, we first analyze the impact on the headcount index when different sampling designs are considered. Note that this study is based on real data sets taken from different countries of the European Union, and the empirical measures for comparisons are based on different Monte Carlo simulation studies. For instance, we observe that stratified sampling has the best performance in comparison to alternative sampling designs. Post-stratification performs similar to simple random sampling without replacement, and the use of auxiliary information provides similar results to ones derived from stratified sampling. Second, we also analyze the empirical performance of different variance estimators under the commented sampling designs. We conclude that they have a similar empirical performance, and they provide, in general, confidence intervals with desirable coverage rates.

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Subzar, Mir, Showkat Ahmad Lone, Emmanuel J. Ekpenyong, et al. "Efficient class of ratio cum median estimators for estimating the population median." PLOS ONE 18, no. 2 (2023): e0274690. http://dx.doi.org/10.1371/journal.pone.0274690.

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In estimation theory, the use of auxiliary information significantly improves precision while estimating population parameters. In this paper, an efficient class of ratio cum median estimators of the population median is suggested using simple random sampling without replacement. The expressions for bias and mean square error of the proposed class are derived theoretically. The condition for the asymptotic optimum estimator is obtained with its bias and mean square error expressions. Under certain realistic conditions, the asymptotic optimum estimator is more proficient, based on analytical and numerical comparisons with some existing estimators that are members of the suggested class of estimators. The superiority of the proposed ratio cum median estimators is shown through real data applications. Such a new proposed estimator will be useful in the future for data analysis and making decisions.

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Vozár, Ondřej. "Unbiased Variance Estimator of the Randomised Response Techniques for Population Mean." Statistika: Statistics and Economy Journal 103, no. 1 (2023): 113–20. http://dx.doi.org/10.54694/stat.2022.38.

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Antoch, Mola and Vozár (2022) proposed recently new randomized response technique for population mean or total of a quantitative variable. The aim of the paper is to solve the open problem to derive unbiased variance estimator of these procedures. In their proposal, unlike other randomized response techniques for population mean or total the randomized response is not a linear function of a sensitive variable. However, standard techniques to derive variance estimators in this setting are based on this assumption. That is why an interviewer needs also to know values pseudorandom numbers (i.e., results of individual randomization experiments). Respondents might perceive this relaxation of privacy protection negative. The performance of the approximate two-sided confidence intervals of distributions with different shape including their coverage is assessed by a simulation study for simple random sampling without replacement.

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P. Dibal, Nicholas, and Hamadu Dallah. "Stratified sampling in highly polluted data as an effective and reliable alternative to high breakdown point estimators." Model Assisted Statistics and Applications 16, no. 2 (2021): 109–15. http://dx.doi.org/10.3233/mas-210523.

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Observations on certain real-life cases include units that are incompatible with other data sets. Values that are extreme in nature do influence estimates obtained by conventional estimators. Robust estimators are therefore necessary for efficient estimation of parameters. This paper uses stratification with simple random sampling without replacement to optimize sample allocation in stratum for efficient parameter estimation as an alternative method of handling highly contaminated samples. Our proposed method stratifies the highly contaminated population into two non-overlapping sub-populations, and stratified samples of sizes 50, 200, and 500 was drawn. We estimate the model parameters form the contaminated sampled data using ordinary least squares under the proposed method, and using the two high breakdown point estimators; the Least Median of Squares and Least Trimmed Squares. Our findings shows that the proposed method did not perform well for low contamination levels (⩽ 30%) but outperformed Least Median of Squares and Least Trimmed Squares for higher contamination rates (⩾ 40%). This indicates that our proposed method compares well and compete favorably with the two high breakdown point estimators.

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Jactel, H., N. Perthuisot, P. Menassieu, G. Raise, and C. Burban. "A SAMPLING DESIGN FOR WITHIN-TREE LARVAL POPULATIONS OF THE MARITIME PINE SCALE, MATSUCOCCUS FEYTAUDI DUC. (HOMOPTERA: MARGARODIDAE), AND THE RELATIONSHIP BETWEEN LARVAL POPULATION ESTIMATES AND MALE CATCH IN PHEROMONE TRAPS." Canadian Entomologist 128, no. 6 (1996): 1143–56. http://dx.doi.org/10.4039/ent1281143-6.

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AbstractSampling procedures for estimating within-tree populations of second-stage larvae (L2) of Matsucoccus feytaudi Duc., infesting maritime pine (Pinus pinaster Ait.), were investigated. These included random sampling without replacement, and systematic sampling with and without a linear model. The relative precision of the sampling was affected by the number, size, and bark thickness of the sample units. Because of symmetrical vertical distribution of within-tree populations, systematic sampling with a linear model did not increase precision when compared with simple systematic sampling. Sampling can be profitably reduced to below the crown portion of the bole, after removal of the part with either smooth or very thick and pyramidal bark. Counting L2 exuviae in the upper 10 cm of each 20-cm-long log, using one in every three logs, provided a relative precision of about 40%. The numbers of male M. feytaudi caught in sticky traps baited with 5 or 30 μg of synthetic pheromone were compared with the numbers of L2 estimated according to the sampling method previously developed. There was a significant positive correlation between number of scales caught and L2 estimates, at the level of individual trees for the lower dose lures, and at the level of groups of trees for the higher dose lures, used in 20-year-old stands. Large captures in younger, weakly infested stands were related to a possible immigration of flying scale insects.

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