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Journal articles on the topic 'Weibull method'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Jiajin, Xu. "Using Monte Carlo method to Upgrade Zhentong Gao method." World Journal of Advanced Research and Reviews 22, no. 2 (2024): 633–40. https://doi.org/10.5281/zenodo.14603002.

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In recent decades, it has been found that the three-parament Weibull distribution plays an increasingly important role in the fields such as structural fatigue and reliability. However, the complexity of estimating these three parameters greatly affects the application of the Weibull distribution. In the past three years, the author has successively proposed the Zhentong Gao Method and the Generalized Zhentong Gao Method, which have effectively solved this problem. However, it has also been found that there is room for improvement in these two methods. That's what this paper is about, how to u

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2

Hussain, Sajid, Mahmood Ul Hassan, Muhammad Sajid Rashid, and Rashid Ahmed. "Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution." Mathematics 11, no. 14 (2023): 3090. http://dx.doi.org/10.3390/math11143090.

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In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions are proposed. The expressions for distribution function and density function of BIIIEE-X family are written in terms of linear combinations of the exponentiated densities based to parent model. New models, i.e., Weibul extended exponentiated Weibull (WEEW), Lomax extended exponentiated Weibull (LEEW), Logistic extended exponentiated Weibull (LGCEEW

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3

Gu, Ying Kui, De Liang Ge, and Yao Gang Xiong. "A Reliability Data Analysis Method Using Mixture Weibull Distribution Model." Applied Mechanics and Materials 148-149 (December 2011): 1449–53. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.1449.

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The weibull distribution plays a crucial role in reliability theory and life-testing experiments. Weibull mixtures are widely used to model lifetime and failure time data, since they exhibit a wide range of shapes for the failure rate function. In this paper, the failure data of crank rod system was analyzed by using mixture weibull distribution model. The distribution parameters of the mixture weibull distribution model were estimated by using maximum likelihood estimation and drawing method. The comparison of fitting degree of failure location between standard weibull distribution model and

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4

Oluyede, Broderick. "The Gamma-Weibull-G Family of Distributions with Applications." Austrian Journal of Statistics 47, no. 1 (2018): 45–76. http://dx.doi.org/10.17713/ajs.v47i1.155.

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Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail this new class of distributions, namely, Gamma-WeibullG family of distributions (GWG). Some special models in the new class are discussed. Statistical properties of the family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and ord

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5

Xu, Jiajin. "From Zhentong Gao Method to Generalized Zhentong Gao Method." Journal of Physics: Conference Series 2650, no. 1 (2023): 012013. http://dx.doi.org/10.1088/1742-6596/2650/1/012013.

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Abstract It is found that the data of structural fatigue life are mostly in accordance with Weibull distribution rather than Gaussian distribution, but the biggest obstacle affecting the application of Weibull distribution is that the estimation of its three- parameters will encounter difficulties in mathematical derivation and complicated calculation. Based on the estimation of correlation coefficient, the author has proposed Zhentong Gao method (Z.T. Gao method) which can avoid these difficulties. Further research found that the idea of Z.T. Gao method can be used to directly calculate the m

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6

Gu, Ying Kui, and Jing Li. "Engine Failure Data Analysis Method Based on Weibull Distribution Model." Applied Mechanics and Materials 128-129 (October 2011): 850–54. http://dx.doi.org/10.4028/www.scientific.net/amm.128-129.850.

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The failure data of crank rod system was analyzed by using weibull parallel model on the base of the simple weibull method. The distribution parameters of the weibull parallel model were estimated by using drawing method. The solving process of WPP drawing method was given in detial. Results show that the fitting degree of the failure data in the weibull parallel model is higher than that of the simple weibull distribution model, and it can more accurately described the failure distribution curve of the system in life cycle, which can provide necessary information for engine reliability indexe

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7

Alharbi, Talal, and Farag Hamad. "An Optimal Strategy for Estimating Weibull distribution Parameters by Using Maximum Likelihood Method." Statistics, Optimization & Information Computing 12, no. 5 (2024): 1342–51. http://dx.doi.org/10.19139/soic-2310-5070-2019.

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Several methods have been used to estimate the Weibull parameters such as least square method (LSM), weighted least square method (WLSM), method of moments (MOM), and maximum likelihood (MLE). The maximum likelihood method is the most popular method (MLE). Newton-Raphson method has been applied to solve the normal equations of MLE’s in order to estimate the Weibull parameters. The method was used to find the optimal values of the Weibull distribution parameters for which the log-likelihood function is maximized. We tried to find the approximation solution to the normal equations of the MLE’s b

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8

Jiajin Xu. "Using Monte Carlo method to Upgrade Zhentong Gao method." World Journal of Advanced Research and Reviews 22, no. 2 (2024): 633–40. http://dx.doi.org/10.30574/wjarr.2024.22.2.1391.

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In recent decades, it has been found that the three-parament Weibull distribution plays an increasingly important role in the fields such as structural fatigue and reliability. However, the complexity of estimating these three parameters greatly affects the application of the Weibull distribution. In the past three years, the author has successively proposed the Zhentong Gao Method and the Generalized Zhentong Gao Method, which have effectively solved this problem. However, it has also been found that there is room for improvement in these two methods. That's what this paper is about, how to u

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9

Park, Chanseok. "A Note on the Existence of the Location Parameter Estimate of the Three-Parameter Weibull Model Using the Weibull Plot." Mathematical Problems in Engineering 2018 (October 9, 2018): 1–6. http://dx.doi.org/10.1155/2018/6056975.

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The Weibull model is one of the widely used distributions in reliability engineering. For the parameter estimation of the Weibull model, there are several existing methods. The method of the maximum likelihood estimation among others is preferred because of its attractive statistical properties. However, for the case of the three-parameter Weibull model, the method of the maximum likelihood estimation has several drawbacks. To avoid the drawbacks, the method using the sample correlation from the Weibull plot is recently suggested. In this paper, we provide the justification for using this new

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10

Ali, Sajid, Hongbae Park, Adnan Aslam Noon, Aamer Sharif, and Daeyong Lee. "Accuracy Testing of Different Methods for Estimating Weibull Parameters of Wind Energy at Various Heights above Sea Level." Energies 17, no. 9 (2024): 2173. http://dx.doi.org/10.3390/en17092173.

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The Weibull algorithm is one of the most accurate tools for forecasting and estimating wind energy potential. Two main parameters of the Weibull algorithm are the ‘Weibull shape’ and ‘Weibull scale’ factors. There are six different numerical methods to estimate the two Weibull parameters. These six methods are the empirical method of Justus (method 1), the empirical method of Lysen (method 2), the maximum likelihood method (method 3), the modified maximum likelihood method (method 4), the energy pattern factor method (method 5) and the graphical method (method 6). Many commercial wind energy s

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11

Parajuli, Ayush. "Evaluation of weibull parameter estimators for wind speed of Jumla, Nepal." Journal of Engineering Issues and Solutions 1, no. 1 (2021): 1–7. http://dx.doi.org/10.3126/joeis.v1i1.36812.

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Weibull Probability Distribution Function (PDF) is widely used across world for estimation of wind power. Weibull function is a two parameter probability distribution function. The methods employed for the evaluation of these two parameters are critical for the efficient use of Weibull PDF. In the present study, three different Weibull PDF parameter estimators have been evaluated. For this purpose, the daily averaged wind speed data of Jumla Station, Nepal for period of 10 year (2004 – 2014: 2012 excluded) is studied. The parameter estimator evaluated in this study are Method of Moments (MoM),

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12

Thiraphorn, B. L., W. Z. Leow, I. Safwati, et al. "Assessment of wind power potential in the North region of Malaysia, Chuping Perlis." Journal of Physics: Conference Series 2550, no. 1 (2023): 012009. http://dx.doi.org/10.1088/1742-6596/2550/1/012009.

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Abstract The wind turbines is a main device that convert the kinetic energy from blades to electrical energy. Before installing wind turbines, the Weibull probability distribution must be calculated to determine the certain wind speed probability. Many problems will come if there no analysis the characteristics of wind in selected location, such as wind speed that not suitable for building wind farm to supply the population in that area. Shape and scale factors, which be controlled in a variety of ways, influence the Weibull distribution. Many studies have looked into which of the various Weib

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K., Sukkiramathi, and V. Seshaiah C. "Some Characteristics of Weibull Distribution and its Contribution to Wind Energy Analysis." International Journal of Trend in Scientific Research and Development 3, no. 3 (2019): 197–202. https://doi.org/10.31142/ijtsrd21685.

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Weibull distribution is a proper distribution to use in modelling the life time data for more than four decades. The Weibull distribution has been found to be a suitable fit for the empirical distribution of the wind speed measurement samples. In brief this paper consist of presentation of general review of important properties and characters in Weibull distribution. Also we discuss the application of the two parameter Weibull distribution to wind speed measurements. The estimation of unknown parameters in Weibull distribution along with some properties of moment method are also discussed. K.

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14

Lei, Y. "Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis )." Journal of Forest Science 54, No. 12 (2008): 566–71. http://dx.doi.org/10.17221/68/2008-jfs.

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Weibull distribution was used to fit tree diameter data collected from 86 sample plots located in Chinese pine stand in Beijing. To estimate the Weibull distribution parameters, three methods [namely maximum likelihood estimation method (MLE), method of moment (MOM) and least-squares regression method (LSM)] were compared and evaluated on the basis of the mean square error (MSE) and sample size. For these sample plots, the moment method was superior for estimating the parameters of Weibull distribution for tree diameter distribution.

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15

Rangoli, A. M., and A. S. Talawar. "Inference on modified Weibull type distribution and its application to Competing risks data using MCMC." INTERNATIONAL JOURNAL OF AGRICULTURAL AND STATISTICAL SCIENCES 20, no. 02 (2024): 333. https://doi.org/10.59467/ijass.2024.20.333.

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For lifetime data analysis, failure time analysis, or survival analysis, the Weibull distribution is commonly used due to its various hazard functions, which can be increasing, decreasing, or constant. We have extended the traditional twoparameter Weibull distribution to accommodate hazard functions that are increasing, decreasing, constant and bathtubshaped. Utilizing a competing risks approach, we applied this modified Weibull distribution to both simulated data and an observed mice dataset. Our findings indicate that the modified Weibull distribution provides a better fit to the mice datase

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16

Ono, Kanji. "A Simple Estimation Method of Weibull Modulus and Verification with Strength Data." Applied Sciences 9, no. 8 (2019): 1575. http://dx.doi.org/10.3390/app9081575.

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This study examines methods for simplifying estimation of the Weibull modulus. This parameter is an important instrument in understanding the statistical behavior of the strength of materials, especially those of brittle solids. It is shown that a modification of Robinson’s approximate expression can provide good estimates of Weibull modulus values (m) in terms of average strength (<σ>) and standard deviation (S): m = 1.10 <σ>/S. This modified Robinson relation is verified on the basis of 267 Weibull analyses accompanied by <σ> and S measurements. Estimated m values matched n

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17

Mahdi Salih, Ahmed, and Murtadha Mansour Abdullah. "Comparison between classical and Bayesian estimation with joint Jeffrey’s prior to Weibull distribution parameters in the presence of large sample conditions." Statistics in Transition new series 25, no. 4 (2024): 191–202. https://doi.org/10.59139/stattrans-2024-010.

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Weibull distribution has been considered one of the most common and valuable distributions for building and analyzing good models for lifetime data. Many researchers have studied the properties of Weibull distribution, also in search of the best method to estimate both parameters. In this paper, we proposed a comparison of Weibull distribution parameters under large sample conditions. We chose to study the classical estimation methods of Weibull distribution parameters, including the maximum likelihood estimator and moments estimation (ME). Next, we compared these methods with the Bayesian est

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18

Boroiu, A., V. Nicolae, O. Alssadi, and T. Udma. "Proposal of an analytical method based on linear regression for modeling reliability by Weibull law." IOP Conference Series: Materials Science and Engineering 1220, no. 1 (2022): 012029. http://dx.doi.org/10.1088/1757-899x/1220/1/012029.

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Abstract The paper aims to identify a sufficiently precise and easy method that will ultimately lead to a working tool easily accessible and used for modeling reliability through the most widely used mathematical law in the field of reliability - the Weibull law. An analytical method for linearizing the Weibull function is proposed in order to allow, by using the linear regression function of the Microsoft Office software, to obtain the parameters of the reliability model. The calculation program created in Microsoft Excel allows the identification of the 3 parameters of the Weibull model and

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19

Tizgui, Ijjou, Fatima El Guezar, Hassane Bouzahir, and Brahim Benaid. "Comparison of methods in estimating Weibull parameters for wind energy applications." International Journal of Energy Sector Management 11, no. 4 (2017): 650–63. http://dx.doi.org/10.1108/ijesm-06-2017-0002.

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Purpose The purpose of this study is to select the most accurate and the most efficient method in estimating Weibull parameters at Agadir region in Morocco. Design/methodology/approach In this paper, Weibull distribution is used to model the wind speed in hourly time series format. Since several methods are used to adjust the Weibull distribution to the measured data, in reporting and analyzing the easiest and the most effective method, seven methods have been investigated, namely, the graphical method (GM), the maximum likelihood method (MLM), the empirical method of Justus (EMJ), the empiric

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20

Feng, Zhen Yu, Ke Yi Mao, and Tian Chun Zou. "Comparison of Conservatism on Applying Statistical Analysis Method to Determine Composite Allowance." Applied Mechanics and Materials 117-119 (October 2011): 930–35. http://dx.doi.org/10.4028/www.scientific.net/amm.117-119.930.

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In this paper, composite static strength test are analyzed with the Weibull and normal statistical method. Compare the Weibull analysis with the normal analysis, which shows that the A-basis value and B-basis value from the Weibull analysis respectively are less than ones from normal analysis by approximate 9.7% and 2.6% under tension loading, on the other hand they are decreased by approximate 16.1% and 5.2% under compression loading. This analysis result has the higher application worth.

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Dei Alibazah, Terra, Agung Prabowo, and Bambang Hendriva Guswanto. "Weibull Mortality Tables based on Indonesian Mortality Table 2019." International Journal of Mathematics, Statistics, and Computing 1, no. 4 (2023): 76–83. http://dx.doi.org/10.46336/ijmsc.v1i4.38.

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Life tables are used to calculate the probability that a member of a population for each age group in a certain country would survive until the next year and die before the next year. A life table could be constructed based on another life table using a mortality law. This study will construct a Weibull Life Table based on the 2019 Indonesian Life Table using Weibull’s mortality law, with its parameters estimated using the Ordinary Least Squares method. The results of this study show that the oldest age in the male Weibull Life Table is 115 years, which is 4 years older than the oldest age in

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DEVI, AYU EKA FANNY, I. NYOMAN WIDANA, and KETUT JAYANEGARA. "PENENTUAN CADANGAN PREMI ASURANSI DWIGUNA MENGGUNAKAN METODE ILLINOIS BERDASARKAN HUKUM MORTALITAS WEIBULL." E-Jurnal Matematika 10, no. 4 (2021): 229. http://dx.doi.org/10.24843/mtk.2021.v10.i04.p347.

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Endowment insurance provides protection benefit and saving benefits. In the endowment insurance the insured party (insurance participant) must be paid the premiums. In addition to premiums, there is also policy value, which is sum of money that must be collected by the company in preparation for claim payment. The purpose of this study was to determine calculation of policy value in endowment insurance using Illinois method based on Weibull Mortality Law. In this study used secondary data from United States Life Table in the form of mortality probability data. Calculation value using Weibull m

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Schmidt, Luciane Naimeke, Mateus Niroh Inoue Sanquetta, John Paul McTague, et al. "On the use of the Weibull distribution in modeling and describing diameter distributions of clonal eucalypt stands." Canadian Journal of Forest Research 50, no. 10 (2020): 1050–63. http://dx.doi.org/10.1139/cjfr-2020-0051.

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Weibull distributions have been widely used to describe tree stem diameter distributions. However, there is a scarcity of studies that suggest the best Weibull formulation. The parameters of the Weibull distribution are usually predicted by either the parameter prediction method (PPM) or the parameter recovery method (PRM), although other methods have been proposed. Thus, this study aimed to evaluate the performance of eight Weibull formulations and compare methods of parameter prediction to describe diameter distributions of clonal eucalypt stands in Brazil. Data originated from remeasurement

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Konečná, Tereza, and Zuzana Hübnerová. "Asymptotic Comparison of Parameters Estimates of Two-parameter Weibull Distribution." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 67, no. 1 (2019): 253–63. http://dx.doi.org/10.11118/actaun201967010253.

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The Weibull distribution is frequently applied in various fields, ranging from economy, business, biology, to engineering. This paper aims at estimating the parameters of two-parameter Weibull distribution are determined. For this purpose, the method of quantiles (three different choices of quantiles) and Weibull probability plot method is utilized. The asymptotic covariance matrix of the parameter estimates is derived for both methods. For optimal random choices of quantiles, the variance, covariance and generalized variance is computed. The main contribution of this study is the introduction

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Panduwinata, Hesty Dwiyugo, Suyitno Suyitno, and Moh Nurul Huda. "Model Regresi Weibull Pada Data Kontinu yang Diklasifikasikan." EKSPONENSIAL 13, no. 2 (2022): 123. http://dx.doi.org/10.30872/eksponensial.v13i2.1051.

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Weibull Regression is a model of regression developed from Weibull distribution in which scale parameter is expressed in the regression parameters. The Weibull regression models discussed in this study are the Weibull survival regression, Weibull hazard regression and regression model for the mean. The Weibull survival regression model is a model of the probability that the Mahakam River water is polluted. The Weibull hazard regression model is a model of velocity of the polluted Mahakam River water, and the Weibull regression for the mean is the model used to predict the average value of BOD

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Ahmed, Samir Badawi, Hajar Yusoff Siti, Mohammed Zyoud Alhareth, et al. "Data bank: nine numerical methods for determining the parameters of weibull for wind energy generation tested by five statistical tools." International Journal of Power Electronics and Drive System (IJPEDS) 12, no. 2 (2021): 1114–30. https://doi.org/10.11591/ijpeds.v12.i2.pp1114-1130.

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This study aims to determine the potential of wind energy in the mediterranean coastal plain of Palestine. The parameters of the Weibull distribution were calculated on basis of wind speed data. Accordingly, two approaches were employed: analysis of a set of actual time series data and theoretical Weibull probability function. In this analysis, the parameters Weibull shape factor ‘k’ and the Weibull scale factor ‘c’ were adopted. These suitability values were calculated using the following popular methods: method of moments (MM), standard deviation method (STDM), empiri

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Oyewole, J. A., F. O. Aweda, and D. Oni. "Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria." Nigerian Journal of Basic and Applied Sciences 27, no. 2 (2020): 8–15. http://dx.doi.org/10.4314/njbas.v27i2.2.

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There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interes

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Dong, Xiaowei, Feng Sun, Fangchao Xu, et al. "Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm." Mathematics 10, no. 22 (2022): 4337. http://dx.doi.org/10.3390/math10224337.

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The hybrid Weibull distribution model can describe the failure rules of electromechanical products more accurately than the single Weibull distribution model, and it can improve the accuracy of reliability analysis. However, the hybrid Weibull distribution model is also more complex, and the multi-parameter estimation is more difficult. In this paper, a reliability mathematical model based on the two-fold three-parameter hybrid Weibull distribution model was established, an EM optimization algorithm was derived for its solution, and a practical initial parameter selection scheme was designed.

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Shoaib, Muhammad, Imran Siddiqui, Saif Ur Rehman, and Ibrahim Zia. "Wind Energy Potential Assessment for Nooriabad Sindh Pakistan." International Journal of Economic and Environmental Geology 10, no. 4 (2020): 78–83. http://dx.doi.org/10.46660/ijeeg.vol10.iss4.2019.357.

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Wind speeds recorded at regular intervals of time for a particular wind site correspond to intermittent sourceof energy. Reliable estimate of wind potential for the site requires fitting of the recorded data to a continuousdistribution function. Weibull function with two parameters is widely used mathematical function for fitting wind speeddata for the estimation of wind energy. In the present study, analysis on the data registered in steps of 1 minute intervalfor the years of 2003 and 2004 for Nooriabad, Sindh were carried out. Recorded data set contains wind speeds andwind directions at 30 m

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Shoaib, Muhammad, Imran Siddiqui, Saif Ur Rehman, and Ibrahim Zia. "Wind Energy Potential Assessment for Nooriabad Sindh Pakistan." International Journal of Economic and Environmental Geology 10, no. 4 (2020): 78–83. http://dx.doi.org/10.46660/ojs.v10i4.357.

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Wind speeds recorded at regular intervals of time for a particular wind site correspond to intermittent sourceof energy. Reliable estimate of wind potential for the site requires fitting of the recorded data to a continuousdistribution function. Weibull function with two parameters is widely used mathematical function for fitting wind speeddata for the estimation of wind energy. In the present study, analysis on the data registered in steps of 1 minute intervalfor the years of 2003 and 2004 for Nooriabad, Sindh were carried out. Recorded data set contains wind speeds andwind directions at 30 m

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Cao, Quang V. "A Method to Distribute Mortality in Diameter Distribution Models." Forest Science 43, no. 3 (1997): 435–42. http://dx.doi.org/10.1093/forestscience/43.3.435.

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Abstract Bailey (1980) derived tree diameter growth models by transforming variables which preserved the functional form of the probability density function that approximated diameter distributions. The necessary assumption was either no mortality, or that mortality was proportionally distributed among diameter classes. The latter assumption might not be realistic since smaller trees should suffer more from competition than large trees and are more likely to die. This paper deals with the case when mortality is not proportionally distributed. If diameters in a stand originally follow a Weibull

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Badawi, Ahmed Samir, Siti Hajar Yusoff, Alhareth Mohammed Zyoud, et al. "Data bank: nine numerical methods for determining the parameters of weibull for wind energy generation tested by five statistical tools." International Journal of Power Electronics and Drive Systems (IJPEDS) 12, no. 2 (2021): 1114. http://dx.doi.org/10.11591/ijpeds.v12.i2.pp1114-1130.

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This study aims to determine the potential of wind energy in the mediterranean coastal plain of Palestine. The parameters of the Weibull distribution were calculated on basis of wind speed data. Accordingly, two approaches were employed: analysis of a set of actual time series data and theoretical Weibull probability function. In this analysis, the parameters Weibull shape factor ‘<em>k</em>’ and the Weibull scale factor ‘<em>c</em>’ were adopted. These suitability values were calculated using the following popular methods: method of moments (MM), standard deviation met

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GÜL, Hasan Hüseyin. "Unit-Weibull Distribution: Different Method of Estimations." Karadeniz Fen Bilimleri Dergisi 13, no. 2 (2023): 547–60. http://dx.doi.org/10.31466/kfbd.1239446.

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Recently, the unit-Weibull (UW) distribution, which is used quite effectively in analyzing lifetime data. The main goal of this article is to investigate the performance of seven estimation methods namely, maximum likelihood (ML), least square (LS), weighted least square (WLS), Anderson-Darling (AD), right-tail Anderson-Darling (RAD), Cramer-von-Mises (CVM) and percentile (PCE) for parameter estimation. An extensive Monte Carlo simulation study is considered to compare the performances of these methods through biases and mean square errors (MSEs). The numerical results show that the PCE estima

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Tahir, Muhammad H., Muhammad Adnan Hussain, Gauss M. Cordeiro, M. El-Morshedy, and M. S. Eliwa. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension." Mathematics 8, no. 11 (2020): 1989. http://dx.doi.org/10.3390/math8111989.

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For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called t

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Chairina, Puspa, Suyitno Suyitno, and Meiliyani Siringoringo. "Model-Model Regresi Weibull Univariat pada Indikator Pencemaran Air Dissolved Oxygen di Daerah Aliran Sungai Lingkungan Hutan Hujan Tropis Kalimantan Timur." EKSPONENSIAL 11, no. 1 (2021): 19. http://dx.doi.org/10.30872/eksponensial.v11i1.641.

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A Univariate Weibull Regression is a model of regression developed from univariate Weibull distribution with the parameter scale is stated in parameter regression. There are some of univariate Weibull regression model, namely Weibull survival regression, Weibull hazard regression and mean model. Univariate Weibull regression model in this research is applied to the water pollution indicator dissolved oxygen (DO data at Mahakam river in East Kalimantan. The purpose of this study is to find out the model of univariate Weibull regression based on the parameter estimation by using maximum likeliho

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Khan, Mohammad Golam Mostafa, and Mohammed Rafiuddin Ahmed. "Bayesian method for estimating Weibull parameters for wind resource assessment in a tropical region: a comparison between two-parameter and three-parameter Weibull distributions." Wind Energy Science 8, no. 8 (2023): 1277–98. http://dx.doi.org/10.5194/wes-8-1277-2023.

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Abstract. The two-parameter Weibull distribution has garnered much attention in the assessment of wind energy potential. The estimation of the shape and scale parameters of the distribution has brought forth a successful tool for the wind energy industry. However, it may be inappropriate to use the two-parameter Weibull distribution to assess energy at every location, especially at sites where low wind speeds are frequent, such as in tropical regions. In this work, a robust technique for wind resource assessment using a Bayesian approach for estimating Weibull parameters is first proposed. Sec

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Hussain, Iqrar, Aun Haider, Zahid Ullah, Mario Russo, Giovanni Mercurio Casolino, and Babar Azeem. "Comparative Analysis of Eight Numerical Methods Using Weibull Distribution to Estimate Wind Power Density for Coastal Areas in Pakistan." Energies 16, no. 3 (2023): 1515. http://dx.doi.org/10.3390/en16031515.

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Currently, Pakistan is facing severe energy crises and global warming effects. Hence, there is an urgent need to utilize renewable energy generation. In this context, Pakistan possesses massive wind energy potential across the coastal areas. This paper investigates and numerically analyzes coastal areas’ wind power density potential. Eight different state-of-the-art numerical methods, namely an (a) empirical method, (b) graphical method, (c) wasp algorithm, (d) energy pattern method, (e) moment method, (f) maximum likelihood method, (g) energy trend method, and (h) least-squares regression met

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Aristone, Flavio, Amaury de Souza, Ivana Pobocikova, et al. "Evaluation of Weibull parameters by different methods for farms." Acta Scientiarum. Technology 46, no. 1 (2023): e64999. http://dx.doi.org/10.4025/actascitechnol.v46i1.64999.

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One of the most prevalent clean and sustainable forms of energy produced worldwide is the power created from wind runoff. Wind turbines ought to be installed in areas with favorable circumstances to transform mechanical wind energy into electricity. Finding appropriate ways to predict the energy produced by a wind farm using the Weibull distribution is the main goal of this work. Theoretical techniques have been applied to calculate Weibull selected characteristics using experimental data gathered at the campus of Universidade Federal de Mato Grosso do Sul (UFMS) in Brazil. These data were gat

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Azizah, Nur, Suyitno Suyitno, and Memi Nor Hayati. "Pemodelan Laju Kematian Pasien Covid-19 di RSUD Abdul Wahab Sjahranie Samarinda menggunakan Model Regresi Weibull." Journal of Mathematics Computations and Statistics 6, no. 1 (2023): 17. http://dx.doi.org/10.35580/jmathcos.v6i1.36379.

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Model regresi Weibull adalah pengembangan dari distribusi Weibull, yakni distribusi Weibull yang dipengaruhi langsung oleh kovariat. Model-model regresi Weibull yang dibahas pada penelitian ini adalah model regresi survival Weibull dan regresi hazard Weibull. Model regresi Weibull pada penelitian ini diaplikasikan pada data waktu pasien penderita penyakit COVID-19 di RSUD Abdul Wahab Sjahranie Samarinda tahun 2021. Event penelitian ini adalah kematian pasien COVID-19. Tujuan penelitian ini adalah mengetahui model regresi survival Weibull dan regresi hazard Weibull pada data waktu rawat inap pa

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Shi, Yan Yan, Zhi Li Sun, Guo Quan Li, and Feng Mu. "The Method of Analyzing the Reliability of Tooth Surface Contact Strength Based on Finite Element Method and Weibull Distribution." Applied Mechanics and Materials 16-19 (October 2009): 363–67. http://dx.doi.org/10.4028/www.scientific.net/amm.16-19.363.

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In this paper, a method of analyzing the reliability of tooth surface contact strength was presented and several kinds of errors of tooth shape were taken into consideration. In the method, experimental design method and Finite Element Method (FEM) were used to get the samples of tooth surface contact stress, and then Weibull distribution was used to fit these samples. On the basis of both stress and strength obeying to Weibull distribution, the reliability of tooth surface contact strength was calculated. The result of the calculation example indicates that the method is correct and effective

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Saleem, Sehar, Rehan Ahmad Khan Sherwani, Muhammad Amin, Maryam Khalid, and Nouman Ali. "Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models." Mathematical Problems in Engineering 2021 (May 25, 2021): 1–15. http://dx.doi.org/10.1155/2021/1953546.

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A popular robust estimation technique for linear models is the rank-based method as an alternative to the ordinary least square (OLS) and restricted maximum likelihood (REML) in the presence of extreme observations. This method is applied in machine reliability analysis and quantum engineering, especially in artificial intelligence and optimization problems where outliers are commonly observed. This technique is also extended for the multilevel model, where the shape of error distribution contributes a significant role in more efficient estimation. In this study, we proposed the Weibull score

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Vega-Zuñiga, Samuel, Juan Gabriel Rueda-Bayona, and Adalberto Ospino-Castro. "Evaluation of Eleven Numerical Methods for Determining Weibull Parameters for Wind Energy Generation in the Caribbean Region of Colombia." Mathematical Modelling of Engineering Problems 09, no. 01 (2022): 194–99. http://dx.doi.org/10.18280/mmep.090124.

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The two-parameter Weibull probability density function (PDF) is widely utilized by different researchers and engineers to fit wind speed data for statistical analysis and modeling. The characterization of wind resources in the frequency and probability domain is necessary to estimate the power output potential of new wind energy projects. Considering that exist a variety of Weibull equations evidenced in the literature review, this article evaluates 11 different methods to calculate the shape and scale parameters of the Weibull PDF. In this sense, it was written an algorithm within a Matlab fu

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Alshanbari, Huda M., Gadde Srinivasa Rao, Jin-Taek Seong, and Saima K. Khosa. "A New Sine-Based Distributional Method with Symmetrical and Asymmetrical Natures: Control Chart with Industrial Implication." Symmetry 15, no. 10 (2023): 1892. http://dx.doi.org/10.3390/sym15101892.

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Control charts are widely used in quality control and industrial sectors. Because of their important role, researchers are focusing on the development of new control charts. According to our study, there is no significant amount of published work on control charts using trigonometrically generated distribution methods. In this paper, we contribute to this interesting research gap by developing a new control chart using a sine-based distributional method. The proposed distributional method (or family of probability distributions) may be called a new modified sine-G family of distributions. Base

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Ihaddadene, Razika, Nabila Ihaddadene, and Marouane Mostefaoui. "Estimation of monthly wind speed distribution basing on hybrid Weibull distribution." World Journal of Engineering 13, no. 6 (2016): 509–15. http://dx.doi.org/10.1108/wje-09-2016-0084.

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Purpose The purpose of this paper is to analyze and compare four numerical methods to estimate the most suitable one which describes wind speed distribution of M’Sila, a province of northern Algeria. Design/methodology/approach The site chosen in this investigation is characterized by calm winds; in this case, the appropriate wind speed distribution is that of hybrid Weibull. Findings The four numerical methods used in the present paper are the maximum likelihood method, the graphical method, the moment method and the energy pattern factor method. The hybrid Weibull distributions using the abo

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Xu, Jiajin. "Bayesian Method for Determining the Three Parameters of Weibull Distribution." Journal of Physics: Conference Series 2890, no. 1 (2024): 012014. http://dx.doi.org/10.1088/1742-6596/2890/1/012014.

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Abstract In recent decades, it has been found that the three parameter Weibull distribution plays an increasingly important role in the fields of structural fatigue and reliability. However, due to the complexity of the methods for estimating these three parameters, the application of the three parameter Weibull distribution has been greatly affected. The author has successively proposed the Zhentong Gao method and the generalized Zhentong Gao method in recent years, which have better solved this problem. Later, by using the characteristics of the Monte Carlo method and the Metropolis-Hastings

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Salsinha, Cecilia Novianti, Yeni Rafita Sihombing, and Melissa Aeudia Daullu. "Bayesian Method for Quality Control with Weibull Distribution." RANGE: Jurnal Pendidikan Matematika 6, no. 1 (2024): 138–52. http://dx.doi.org/10.32938/jpm.v6i1.7178.

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Weibull distribution is one of the continous probability density function. This distribution is known as a flexible distribution. One of it’s flexibility is can be transformed into other distributions such as exponential distribution depends on parameter selected. Similar to other distribution, Weibull distribution also characterized by cumulative distribution function, mean, variance and moment generating function. One of the well-known application of this distribution is in the field of quality control utilizing reliability data and the well-known tool in quality control is control chart. Th

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Aminu Adamu, Abubakar Yahaya, and Hussaini Garba Dikko. "APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS." FUDMA JOURNAL OF SCIENCES 5, no. 2 (2021): 89–99. http://dx.doi.org/10.33003/fjs-2021-0502-479.

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In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbi

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Shah, Zubir, Dost Muhammad Khan, Zardad Khan, et al. "A New Generalized Logarithmic–X Family of Distributions with Biomedical Data Analysis." Applied Sciences 13, no. 6 (2023): 3668. http://dx.doi.org/10.3390/app13063668.

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In this article, an attempt is made to propose a novel method of lifetime distributions with maximum flexibility using a popular T–X approach together with an exponential distribution, which is known as the New Generalized Logarithmic-X Family (NGLog–X for short) of distributions. Additionally, the generalized form of the Weibull distribution was derived by using the NGLog–X family, known as the New Generalized Logarithmic Weibull (NGLog–Weib) distribution. For the proposed method, some statistical properties, including the moments, moment generating function (MGF), residual and reverse residu

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Klakattawi, Hadeel S. "The Weibull-Gamma Distribution: Properties and Applications." Entropy 21, no. 5 (2019): 438. http://dx.doi.org/10.3390/e21050438.

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A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

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El-Morshedy, Mahmoud, Zubair Ahmad, Elsayed tag-Eldin, Zahra Almaspoor, Mohamed S. Eliwa, and Zahoor Iqbal. "A new statistical approach for modeling the bladder cancer and leukemia patients data sets: Case studies in the medical sector." Mathematical Biosciences and Engineering 19, no. 10 (2022): 10474–92. http://dx.doi.org/10.3934/mbe.2022490.

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<abstract><p>Statistical methods are frequently used in numerous healthcare and other related sectors. One of the possible applications of the statistical methods is to provide the best description of the data sets in the healthcare sector. Keeping in view the applicability of statistical methods in the medical sector, numerous models have been introduced. In this paper, we also introduce a novel statistical method called, a new modified-$ G $ family of distributions. Several mathematical properties of the new modified-$ G $ family are derived. Based on the new modified-$ G $ metho

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