Статті в журналах: "Distribution des applications"

1

Liebrock, Lorie M., and Ken Kennedy. "Automatic Data Distribution for Composite Grid Applications." Scientific Programming 6, no. 1 (1997): 95–113. http://dx.doi.org/10.1155/1997/174748.

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Problem topology is the key to efficient parallelization support for partially regular applications. Specifically, problem topology provides the information necessary for automatic data distribution and regular application optimization of a large class of partially regular applications. Problem topology is the connectivity of the problem. This research focuses on composite grid applications and strives to take advantage of their partial regularity in the parallelization and compilation process. Composite grid problems arise in important application areas, e.g., reactor and aerodynamic simulation. Related physical phenomena are inherently parallel and their simulations are computationally intensive. We present algorithms that automatically determine data distributions for composite grid problems. Our algorithm's alignment and distribution specifications may be used as input to a High Performance Fortran program to apply the mapping for execution of the simulation code. These algorithms eliminate the need for user-specified data distribution for this large class of complex topology problems. We test the algorithms using a number of topological descriptions from aerodynamic and water-cooled nuclear reactor simulations. Speedup-bound predictions with and without communication, based on the automatically generated distributions, indicate that significant speedups are possible using these algorithms.

2

Sarabia, José María, Vanesa Jordá, Faustino Prieto, and Montserrat Guillén. "Multivariate Classes of GB2 Distributions with Applications." Mathematics 9, no. 1 (December 31, 2020): 72. http://dx.doi.org/10.3390/math9010072.

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The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and insurance. In this paper, several multivariate classes of the GB2 distribution are proposed. The different multivariate versions are based on two simple univariate representations of the GB2 distribution. The first type of multivariate distributions are constructed from a stochastic dependent representations defined in terms of gamma random variables. Using this representation and beginning by two particular multivariate GB2 distributions, multivariate Singh–Maddala and Dagum income distributions are presented and several properties are obtained. Then, a general multivariate GB2 distribution is introduced. The second type of multivariate distributions are based on a generalization of the distribution of the order statistics, which gives place to multivariate GB2 distribution with support above the diagonal. We discuss the role of these families in modeling bivariate income distributions. Finally, an empirical application is given, where we show that a multivariate GB2 distribution can be useful for modeling compound precipitation and wind events in the whole range.

3

Nassar, Mazen, Sanku Dey, and Devendra Kumar. "Logarithm Transformed Lomax Distribution with Applications." Calcutta Statistical Association Bulletin 70, no. 2 (November 2018): 122–35. http://dx.doi.org/10.1177/0008068318808135.

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In this article, we introduce a new method for generating distributions which we refer to as logarithm transformed (LT) method. Some statistical properties of the LT method are established. Based on the LT method, we introduce a new generalization of the Lomax distribution that provides better fits than the Lomax distribution and some of its known generalizations. We refer to the new distribution as logarithmic transformed Lomax (LTL) distribution. Various properties of the LTL distribution, including explicit expressions for the moments, quantiles, moment generating function, incomplete moments, conditional moments, Rényi entropy, and order statistics are derived. It appears to be a distribution capable of allowing monotonically decreasing and upside-down bathtub shaped hazard rates depending on its parameters, so it turns out to be quite flexible for analysing non-negative real life data. We discuss the estimation of the model parameters by maximum likelihood method using random censoring scheme. The proposed distribution is utilized to fit a censored data set and the distribution is shown to be more appropriate to the data set than the compared distributions. 2010 Mathematics Subject Classification: 60E05, 60E10, 62E15.

4

Rather, N. A., and T. A. Rather. "New Generalizations of Exponential Distribution with Applications." Journal of Probability and Statistics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/2106748.

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The main purpose of this paper is to present k-Generalized Exponential Distribution which among other things includes Generalized Exponential and Weibull Distributions as special cases. Besides, we also obtain three-parameter extension of Generalized Exponential Distribution. We shall also discuss moment generating functions (MGFs) of these newly introduced distributions.

5

Badmus, N. I., Olanrewaju Faweya, and K. A. Adeleke. "Generalized Beta-Exponential Weibull Distribution and its Applications." Journal of Statistics: Advances in Theory and Applications 24, no. 1 (December 10, 2020): 1–33. http://dx.doi.org/10.18642/jsata_7100122158.

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In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

6

Klakattawi, Hadeel S. "The Weibull-Gamma Distribution: Properties and Applications." Entropy 21, no. 5 (April 26, 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.

7

Hassan, Anwar, and Peer Bilal Ahmad. "Misclassified size-biased modified power series distribution and its applications." Mathematica Bohemica 134, no. 1 (2009): 1–17. http://dx.doi.org/10.21136/mb.2009.140633.

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8

Boonthiem, Somchit, Adisak Moumeesri, Watcharin Klongdee, and Weenakorn Ieosanurak. "A New Sushila Distribution: Properties and Applications." European Journal of Pure and Applied Mathematics 15, no. 3 (July 31, 2022): 1280–300. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4420.

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In this paper, we introduce a new continuous distribution mixing exponential and gamma distributions, called new Sushila distribution. We derive some properties of the distribution include: probability density function, cumulative distribution function, expected value, moments about the origin, coefficient of variation (C.V.), coefficient of skewness, coefficient of kurtosis, moment generating function, and reliability measures. The distribution includes, a special cases, the Sushila distribution as a particular case p=1/2 (θ = 1). The hazard rate function exhibits increasing. The parameter estimations as the moment estimation (ME), the maximum likelihood estimation (MLE), nonlinear least squares methods, and genetic algorithm (GA) are proposed. The application is presented to show that model to fit for waiting time and survival time data. Numerical results compare ME, MLE, weighted least squares (WLS), unweighted least squares (UWLS), and GA. The results conclude that GA method is better performance than the others for iterative methods. Although, ME is not the best estimate, ME is a fast estimate, because it is not an iterative method. Moreover, The proposed distribution has been compared with Lindley and Sushila distributions to a waiting time data set. The result shows that the proposed distribution is performing better than Lindley and Sushila distribution.

9

Rasekhi, Mahdi, Omid Chatrabgoun, and Alireza Daneshkhah. "Discreteweighted exponential distribution: Properties and applications." Filomat 32, no. 8 (2018): 3043–56. http://dx.doi.org/10.2298/fil1808043r.

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In this paper, we propose a new lifetime model as a discrete version of the continuous weighted exponential distribution which is called discrete weighted exponential distribution (DWED). This model is a generalization of the discrete exponential distribution which is originally introduced by Chakraborty (2015). We present various statistical indices/properties of this distribution including reliability indices, moment generating function, probability generating function, survival and hazard rate functions, index of dispersion, and stress-strength parameter. We first present a numerical method to compute the maximum likelihood estimations (MLEs) of the models parameters, and then conduct a simulation study to further analyze these estimations. The advantages of the DWED are shown in practice by applying it on two real world applications and compare it with some other well-known lifetime distributions.

10

U., Eric, Oti M.O.O., and Francis C.E. "A Study of Properties and Applications of Gamma Distribution." African Journal of Mathematics and Statistics Studies 4, no. 2 (July 8, 2021): 52–65. http://dx.doi.org/10.52589/ajmss-mr0dq1dg.

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The gamma distribution is one of the continuous distributions; the distributions are very versatile and give useful presentations of many physical situations. They are perhaps the most applied statistical distribution in the area of reliability. In this paper, we present the study of properties and applications of gamma distribution to real life situations such as fitting the gamma distribution into data, burn-out time of electrical devices and reliability theory. The study employs the moment generating function approach and the special case of gamma distribution to show that the gamma distribution is a legitimate continuous probability distribution showing its characteristics.

11

Habib, Elsayed Ali. "Estimation of Log-Linear-Binomial Distribution with Applications." Journal of Probability and Statistics 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/423654.

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Log-linear-binomial distribution was introduced for describing the behavior of the sum of dependent Bernoulli random variables. The distribution is a generalization of binomial distribution that allows construction of a broad class of distributions. In this paper, we consider the problem of estimating the two parameters of log-linearbinomial distribution by moment and maximum likelihood methods. The distribution is used to fit genetic data and to obtain the sampling distribution of the sign test under dependence among trials.

12

Aljarrah, Mohammad. "Generalized hyperbolic secant distribution: Properties, estimation, and applications." Filomat 35, no. 13 (2021): 4305–26. http://dx.doi.org/10.2298/fil2113305a.

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In this study, we define a generalized hyperbolic secant distribution. Poor fit to heavy tailed data sets is repeatedly obtained by existing three-parameter distributions. Only three parameters are considered in the proposed new distribution and it fits a heavy left- and right-tailed data better than various existing distributions. We study some properties of the new distribution, namely, mode, skewness, kurtosis, hazard function, moments, mean deviation, and Shannon entropy. Seven different frequentist methods for estimating the parameters are briefly described. A simulation study is also conducted to compare the performances of the proposed methods of estimation. The usefulness of the new model is demonstrated by applying it to fit two real-life data.

13

ARYUYUEN, Sirinapa, and Winai BODHISUWAN. "The Truncated Power Lomax Distribution: Properties and Applications." Walailak Journal of Science and Technology (WJST) 16, no. 9 (November 5, 2018): 655–68. http://dx.doi.org/10.48048/wjst.2019.4542.

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A new truncated distribution, called the truncated power Lomax (TPL) distribution, is proposed. This is a truncated version of the power Lomax distribution. The TPL distribution has increasing and decreasing shapes of the hazard function. Some statistical properties, such as moments, survival, hazard, and quantile functions, are discussed. The maximum likelihood estimation (MLE) is constructed for estimating the unknown parameters of the TPL distribution. Moreover, the distribution has been fitted with real data sets to illustrate the usefulness of the proposed distribution. From the results of the example applications, the TPL distribution provides a consistently better fit than the other distributions, i.e., power Lomax and Lomax.

14

Chaudhary, Arun Kumar, and Vijay Kumar. "Half Cauchy-Modified Exponential Distribution: Properties and Applications." Nepal Journal of Mathematical Sciences 3, no. 1 (August 31, 2022): 47–58. http://dx.doi.org/10.3126/njmathsci.v3i1.44125.

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A new distribution having three parameters using half Cauchy family of distribution named half Cauchy modified exponential distribution is deliberated and studied in this work. Its mathematical and statistical properties are examined. Model parameters of novel distribution are evaluated using least-square, maximum likelihood and Cramer-Von-Mises estimations approaches. R programming software is applied to carry out all of the calculations. To evaluate the new distribution's application and goodness-of-fit test, an actual data set is studied for illustration. The suggested new distribution is performed better as compared to some existing distributions.

15

Gnewuch, Michael, Frances Kuo, Harald Niederreiter, and Henryk Woźniakowski. "Uniform Distribution Theory and Applications." Oberwolfach Reports 10, no. 4 (2013): 2837–917. http://dx.doi.org/10.4171/owr/2013/49.

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16

Shanker, Rama. "SUJATHA DISTRIBUTION AND ITS APPLICATIONS." Statistics in Transition. New Series 17, no. 3 (2016): 391–410. http://dx.doi.org/10.21307/stattrans-2016-029.

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17

Kagermann, Henning. "Distribution of Integrated Business Applications." Business & Information Systems Engineering 1, no. 1 (February 2009): 94–100. http://dx.doi.org/10.1007/s12599-008-0026-z.

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18

Huang, Mei-Ling, and Karen Yuen Fung. "R-distribution and its applications." Communications in Statistics - Simulation and Computation 18, no. 1 (January 1989): 99–119. http://dx.doi.org/10.1080/03610918908812749.

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19

Messaadia, Hamouda, and Halim Zeghdoudi. "Zeghdoudi distribution and its applications." International Journal of Computing Science and Mathematics 9, no. 1 (2018): 58. http://dx.doi.org/10.1504/ijcsm.2018.090722.

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20

Messaadia, Hamouda, and Halim Zeghdoudi. "Zeghdoudi distribution and its applications." International Journal of Computing Science and Mathematics 9, no. 1 (2018): 58. http://dx.doi.org/10.1504/ijcsm.2018.10011726.

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21

Willis, H. L., H. Tram, M. V. Engel, and L. Finley. "Optimization applications to power distribution." IEEE Computer Applications in Power 8, no. 4 (1995): 12–17. http://dx.doi.org/10.1109/67.468295.

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22

Huang, M. L., and K. Y. Fung. "D-distribution and its applications." Statistical Papers 34, no. 1 (December 1993): 143–59. http://dx.doi.org/10.1007/bf02925536.

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23

Ibrahim, Sule, Sani Ibrahim Doguwa, Audu Isah, and Haruna, M. Jibril. "Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution." Journal of Statistical Modelling and Analytics 3, no. 2 (October 15, 2021): 81–94. http://dx.doi.org/10.22452/josma.vol3no2.5.

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Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.

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Nagarjuna, Vasili B. V., R. Vishnu Vardhan, and Christophe Chesneau. "Kumaraswamy Generalized Power Lomax Distributionand Its Applications." Stats 4, no. 1 (January 7, 2021): 28–45. http://dx.doi.org/10.3390/stats4010003.

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In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

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Nagarjuna, Vasili B. V., R. Vishnu Vardhan, and Christophe Chesneau. "Kumaraswamy Generalized Power Lomax Distributionand Its Applications." Stats 4, no. 1 (January 7, 2021): 28–45. http://dx.doi.org/10.3390/stats4010003.

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In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

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Nagarjuna, Vasili B. V., Rudravaram Vishnu Vardhan, and Christophe Chesneau. "Nadarajah–Haghighi Lomax Distribution and Its Applications." Mathematical and Computational Applications 27, no. 2 (April 1, 2022): 30. http://dx.doi.org/10.3390/mca27020030.

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Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made to create a hybrid distribution mixing the functionalities of the Nadarajah–Haghighi and Lomax distributions, namely the Nadarajah–Haghighi Lomax (NHLx) distribution. It can also be thought of as an extension of the exponential Lomax distribution. The NHLx distribution has the features of having four parameters, a lower bounded support, and very flexible distributional functions, including a decreasing or unimodal probability density function and an increasing, decreasing, or upside-down bathtub hazard rate function. In addition, it benefits from the treatable statistical properties of moments and quantiles. The statistical applicability of the NHLx model is highlighted, with simulations carried out. Four real data sets are also used to illustrate the practical applications. In particular, results are compared with Lomax-based models of importance, such as the Lomax, Weibull Lomax, and exponential Lomax models, and it is observed that the NHLx model fits better.

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Nguyen, Nguyen Dinh, and Taehong Kim. "Balanced Leader Distribution Algorithm in Kubernetes Clusters." Sensors 21, no. 3 (January 28, 2021): 869. http://dx.doi.org/10.3390/s21030869.

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Container-based virtualization is becoming a de facto way to build and deploy applications because of its simplicity and convenience. Kubernetes is a well-known open-source project that provides an orchestration platform for containerized applications. An application in Kubernetes can contain multiple replicas to achieve high scalability and availability. Stateless applications have no requirement for persistent storage; however, stateful applications require persistent storage for each replica. Therefore, stateful applications usually require a strong consistency of data among replicas. To achieve this, the application often relies on a leader, which is responsible for maintaining consistency and coordinating tasks among replicas. This leads to a problem that the leader often has heavy loads due to its inherent design. In a Kubernetes cluster, having the leaders of multiple applications concentrated in a specific node may become a bottleneck within the system. In this paper, we propose a leader election algorithm that overcomes the bottleneck problem by evenly distributing the leaders throughout nodes in the cluster. We also conduct experiments to prove the correctness and effectiveness of our leader election algorithm compared with a default algorithm in Kubernetes.

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Chesneau, Christophe, Hassan S. Bakouch, and Muhammad Nauman Khan. "A weighted transmuted exponential distributions with environmental applications." Statistics, Optimization & Information Computing 8, no. 1 (February 17, 2020): 36–53. http://dx.doi.org/10.19139/soic-2310-5070-785.

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In this paper, we introduce a new three-parameter distribution. It is based on the combination of a re-parametrization of a general family of distributions (known as the EGNB2 distribution) and the so-called quadratic rank transmutation map defined with the exponential distribution as baseline. We explore some mathematical properties of this distribution including the hazard rate function, moments, the moment generating function, the quantile function, various entropy measures and (reversed) residual life functions. A statistical study investigates estimation of the parameters using the method of maximum likelihood. The distribution along with other existing distributions are fitted to two environmental data sets and its superior performance is assessed by using some goodness-of-fit tests. As a result, some environmental measures associated with these data are obtained such as the return level and mean deviation about this level.

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Unyime, Patrick Udoudo, and Ette Harrison Etuk. "A New Extension of Quasi Lindley Distribution: Properties and Applications." International Journal of Advanced Statistics and Probability 7, no. 2 (October 24, 2019): 28. http://dx.doi.org/10.14419/ijasp.v7i2.29791.

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In this paper, we introduced and studied the statistical properties of a new distribution called the Marshall-Olkin extended quasi Lindley distribution. Specifically, we derived the crude moment, moment generating function, quantile function, and distributions of order statisticsbased on the distribution. The maximum likelihood point estimation method was used to estimate the parameters of the newly introduced model. Some AR minfication processes were discussed. We illustrated the applicability of the distribution using a real dataset.Keywords: Marshal-Olkin family of distributions; maximum likelihood estimates; minification processes; quasi Lindley distribution; quantile function.

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Kabir, Umar, and Terna Godfrey IEREN. "On the inferences and applications of transmuted exponential Lomax distribution." International Journal of Advanced Statistics and Probability 6, no. 1 (January 13, 2018): 30. http://dx.doi.org/10.14419/ijasp.v6i1.8129.

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This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax distributions.

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Huang, Mei Ling, Vincenzo Coia, and Percy Brill. "A Cluster Truncated Pareto Distribution and Its Applications." ISRN Probability and Statistics 2013 (September 18, 2013): 1–10. http://dx.doi.org/10.1155/2013/265373.

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The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is important, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two real-world examples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and study its properties. We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate the MTPD from a random sample. We apply the MTPD and CTPD to the two examples and compare the proposed method with existing estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation method produce very good fitting distributions with real-world data.

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Mohammed, B. I., Abdulaziz S. Alghamdi, Hassan M. Aljohani, and Md Moyazzem Hossain. "The Novel Bivariate Distribution: Statistical Properties and Real Data Applications." Mathematical Problems in Engineering 2021 (December 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/2756779.

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This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.

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Chesneau, Christophe, Vijay Kumar, Mukti Khetan, and Mohd Arshad. "On a Modified Weighted Exponential Distribution with Applications." Mathematical and Computational Applications 27, no. 1 (February 21, 2022): 17. http://dx.doi.org/10.3390/mca27010017.

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Practitioners in all applied domains value simple and adaptable lifetime distributions. They make it possible to create statistical models that are relatively easy to manage. A novel simple lifetime distribution with two parameters is proposed in this article. It is based on a parametric mixture of the exponential and weighted exponential distributions, with a mixture weight depending on a parameter of the involved distribution; no extra parameter is added in this mixture operation. It can also be viewed as a special generalized mixture of two exponential distributions. This decision is based on sound mathematical and physical reasoning; the weight modification allows us to combine some joint properties of the exponential and weighted exponential distribution, which are known as complementary in several modeling aspects. As a result, the proposed distribution may have a decreasing or unimodal probability density function and possess the demanded increasing hazard rate property. Other properties are studied, such as the moments, Bonferroni and Lorenz curves, Rényi entropy, stress-strength reliability, and mean residual life function. Subsequently, a part is devoted to the associated model, which demonstrates how it can be used in a real-world statistical scenario involving data. In this regard, we demonstrate how the estimated model performs well using five different estimation methods and simulated data. The analysis of two data sets demonstrates these excellent results. The new model is compared to the weighted exponential, Weibull, gamma, and generalized exponential models for performance. The obtained comparison results are overwhelmingly in favor of the proposed model according to some standard criteria.

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Chesneau, Christophe. "On a Logarithmic Weighted Power Distribution: Theory, Modelling and Applications." Journal of Mathematical Sciences: Advances and Applications 67, no. 1 (October 10, 2021): 1–59. http://dx.doi.org/10.18642/jmsaa_7100122214.

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Engineers, economists, hydrologists, social scientists, and behavioural scientists often deal with data belonging to the unit interval. One of the most common approaches for modeling purposes is the use of unit distributions, beginning with the classical power distribution. A simple way to improve its applicability is proposed by the transmuted scheme. We propose an alternative in this article by slightly modifying this scheme with a logarithmic weighted function, thus creating the log-weighted power distribution. It can also be thought of as a variant of the log-Lindley distribution, and some other derived unit distributions. We investigate its statistical and functional capabilities, and discuss how it distinguishes between power and transmuted power distributions. Among the functions derived from the log-weighted distribution are the cumulative distribution, probability density, hazard rate, and quantile functions. When appropriate, a shape analysis of them is performed to increase the exibility of the proposed modelling. Various properties are investigated, including stochastic ordering (first order), generalized logarithmic moments, incomplete moments, Rényi entropy, order statistics, reliability measures, and a list of new distributions derived from the main one are offered. Subsequently, the estimation of the model parameters is discussed through the maximum likelihood procedure. Then, the proposed distribution is tested on a few data sets to show in what concrete statistical scenarios it may outperform the transmuted power distribution.

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Aguilar, Guilherme Aparecido Santos, Fernando A. Moala, and Ricardo Puziol de Oliveira. "Marshall olkin extended exponentiated Gamma distribution and its applications." Model Assisted Statistics and Applications 17, no. 2 (May 23, 2022): 123–41. http://dx.doi.org/10.3233/mas-220015.

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Different methods for obtaining new probability distributions have been introduced in the literature in recent years, for example, (Gupta et al., 1998) proposed an interesting uni-parametric lifetime distribution, Exponentiated Gamma (EG), which hazard function has increasing and bathtub shapes. In this paper, we build a new two-parameters distribution, the Marshall Olkin Extended Exponentiated Gamma (MOEEG) distribution, which is derived from the Marshall-Olkin method and the EG distribution. The hazard function of this new distribution can accommodate monotonic, non-monotonic and unimodal shapes, allowing a better fit to greater data variability. In addition to the great flexibility of fitting the data, it contains only two parameters providing a simple parameter estimation procedure, unlike other distributions proposed in the literature that have three or more parameters. Some properties of the new distribution considered in this paper are presented such as n-th time, r-th moment of residual life, r-thmoment of residual life inverted, stochastic ordering, entropy, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics, and stress-strength parameter. We also apply two different estimation methods, maximum likelihood and Bayesian approach. Real data applications are presented to illustrate the usefulness of this new distribution.

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Salem, Hamdy, and Abd-Elwahab Hagag. "Mathematical properties of the Kumaraswamy-Lindley distribution and its applications." International Journal of Advanced Statistics and Probability 5, no. 1 (March 11, 2017): 17. http://dx.doi.org/10.14419/ijasp.v5i1.7410.

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In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

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John, Chisimkwuo. "Inverse Two-Parameter Lindley Distribution and Its Applications." European Journal of Statistics 2 (April 13, 2022): 10. http://dx.doi.org/10.28924/ada/stat.2.10.

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This paper proposes an Inverse two-parameter Lindley distribution (ITPLD). This is originated from Lindley distribution and two-parameter Lindley distribution. Its mathematical and statistical properties which includes its survival function, hazard rate function, shape characteristics of the density, stochastic ordering, entropy measure, and stress-strength reliability were discussed. The estimation of parameters was carried out using the method of maximum likelihood. Also, in the application of the model, HQIC, BIC, CAIC, AIC, and K.S are used to test for the goodness of fit of the model which was applied to two real data sets. The Inverse two-parameter Lindley distribution was compared with Inverse Lindley, Inverse Akash, and Inverse Exponential distributions in order to determine its superiority.

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Segovia, Francisco A., Yolanda M. Gómez, Osvaldo Venegas, and Héctor W. Gómez. "A Power Maxwell Distribution with Heavy Tails and Applications." Mathematics 8, no. 7 (July 7, 2020): 1116. http://dx.doi.org/10.3390/math8071116.

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In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data.

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Ghosh, Indranil, Sanku Dey, and Devendra Kumar. "Bounded M-O Extended Exponential Distribution with Applications." Stochastics and Quality Control 34, no. 1 (June 1, 2019): 35–51. http://dx.doi.org/10.1515/eqc-2018-0028.

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Abstract In this paper a new probability density function with bounded domain is presented. This distribution arises from the Marshall–Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advantage of not including any additional parameter(s) or special function in its formulation. The new transformed model, called the unit-Marshall–Olkin extended exponential (UMOEE) distribution which exhibits decreasing, increasing and then bathtub shaped density while the hazard rate has increasing and bathtub shaped. Various properties of the distribution (including quantiles, ordinary moments, incomplete moments, conditional moments, moment generating function, conditional moment generating function, hazard rate function, mean residual lifetime, Rényi and δ-entropies, stress-strength reliability, order statistics and distributions of sums, difference, products and ratios) are derived. The method of maximum likelihood is used to estimate the model parameters. A simulation study is carried out to examine the bias, mean squared error and 95 asymptotic confidence intervals of the maximum likelihood estimators of the parameters. Finally, the potentiality of the model is studied using two real data sets. Further, a bivariate extension based on copula concept of the proposed model are developed and some properties of the distribution are derived. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.

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Durham, S., J. Lynch, and W. J. Padgett. "TP2-Orderings and the IFR Property with Applications." Probability in the Engineering and Informational Sciences 4, no. 1 (January 1990): 73–88. http://dx.doi.org/10.1017/s0269964800001467.

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In this paper, TP2 orderings of distributions and of survival functions are considered. It is shown that the first passage time of a Markov process with TP2- ordered transition distributions has an increasing failure rate (IFR). Conditions are also given for which mixtures of IFR distributions are IFR. A formula is obtained for the failure rate when the strength distribution is a function of both load and strength. This formula, in conjunction with the TP2-ordering on the strength survival functions and log-concavity of the strength and load variables, leads to an increasing failure rate for the strength distribution. Finally, two models based on this theory are presented which explain the IFR character of the strength distribution of fibrous composite materials.

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Momenkhan, Faten. "Transmuted extended Lomax distribution with some tractability properties and applications." International Journal of Advanced Statistics and Probability 7, no. 1 (August 1, 2019): 28. http://dx.doi.org/10.14419/ijasp.v7i1.28753.

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Extending or generalizing original distributions create new distributions with some tractability properties and with more flexibility in modeling data. In this paper, the extended Lomax distribution introduced by Ghitany et al. [1] is further extended in a larger family by introducing an additional parameter. We provide a comprehensive description of the mathematical properties of the subject distribution along with its reliability behavior. The problem of the parameter estimation for the proposed distribution is considered based on the maximum likelihood approach. Finally, the usefulness of the transmuted distribution for modeling reliability data is illustrated using a simulation study and a real data set.

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Alfaer, Nada M., Ahmed M. Gemeay, Hassan M. Aljohani, and Ahmed Z. Afify. "The Extended Log-Logistic Distribution: Inference and Actuarial Applications." Mathematics 9, no. 12 (June 15, 2021): 1386. http://dx.doi.org/10.3390/math9121386.

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Actuaries are interested in modeling actuarial data using loss models that can be adopted to describe risk exposure. This paper introduces a new flexible extension of the log-logistic distribution, called the extended log-logistic (Ex-LL) distribution, to model heavy-tailed insurance losses data. The Ex-LL hazard function exhibits an upside-down bathtub shape, an increasing shape, a J shape, a decreasing shape, and a reversed-J shape. We derived five important risk measures based on the Ex-LL distribution. The Ex-LL parameters were estimated using different estimation methods, and their performances were assessed using simulation results. Finally, the performance of the Ex-LL distribution was explored using two types of real data from the engineering and insurance sciences. The analyzed data illustrated that the Ex-LL distribution provided an adequate fit compared to other competing distributions such as the log-logistic, alpha-power log-logistic, transmuted log-logistic, generalized log-logistic, Marshall–Olkin log-logistic, inverse log-logistic, and Weibull generalized log-logistic distributions.

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Alhassan, Abukari. "Gompertz Ampadu Class of Distributions: Properties and Applications." Journal of Probability and Statistics 2022 (April 20, 2022): 1–7. http://dx.doi.org/10.1155/2022/1104330.

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This paper introduces a new generator family of distributions called the Gompertz Ampadu-G family. Based on the generator, the Lomax distribution was modified into Gompertz Ampadu Lomax. The new distribution has a flexible hazard rate function that has upside-down and bathtub shapes, including increasing and decreasing hazard rate functions. The distribution comes with some desirable statistical properties. The distribution is applied to real-life data. Parameter estimates and test statistics show a better fit for the competitive models.

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Radyushkin, A. V. "Theory and applications of parton pseudodistributions." International Journal of Modern Physics A 35, no. 05 (February 20, 2020): 2030002. http://dx.doi.org/10.1142/s0217751x20300021.

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We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator [Formula: see text] of the parton fields is a function [Formula: see text] of Lorentz invariants [Formula: see text], the Ioffe time, and the invariant interval [Formula: see text]. This observation allows to extract the Ioffe-time distribution [Formula: see text] from Euclidean separations [Formula: see text] accessible on the lattice. Another basic feature is the use of the ratio [Formula: see text], that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining [Formula: see text]-dependence of the reduced Ioffe-time distribution [Formula: see text] corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions [Formula: see text] using matching relations. The [Formula: see text]-dependence of [Formula: see text] governs the [Formula: see text]-dependence of parton densities [Formula: see text]. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

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Mathew, Jismi, and Christophe Chesneau. "Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications." Mathematical and Computational Applications 25, no. 4 (October 1, 2020): 65. http://dx.doi.org/10.3390/mca25040065.

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It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.

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Aderoju, Samuel, and Isaac Adeniyi. "On Power Generalized Akash Distribution with Properties and Applications." Journal of Statistical Modelling and Analytics 4, no. 1 (April 20, 2022): 1–13. http://dx.doi.org/10.22452/josma.vol4no1.1.

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A new lifetime model known as power generalized Akash distribution (PGAD), which extends generalized Akash (GA) distribution has been proposed in this paper. The PGAD was inspired by the wide use of the Akash and GA distributions in various applied areas. Some structural characteristics of the new model were studied such as moments, reliability, hazard rate function, survival function, Renyi entropy measure and order statistics. The parameters of the model were obtained via the maximum likelihood estimation method. The flexibility and importance of the new distribution has been illustrated by its applications to two real datasets. Using BIC, AIC and 2Loglikelihood, it is obvious that the PGAD is more effective than Topp-Leone Lomax (TLLo), Generalized Akash (GA), Power Pranav (PP) and Power Transformed Power Inverse Lindley (APTPIL) distributions in modelling real lifetime data.

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Kruisselbrink, Thijs, Myriam Aries, and Alexander Rosemann. "A Practical Device for Measuring the Luminance Distribution." International Journal of Sustainable Lighting 19, no. 1 (June 29, 2017): 75–90. http://dx.doi.org/10.26607/ijsl.v19i1.76.

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Various applications in building lighting such as automated daylight systems, dynamic lighting control systems, lighting simulations, and glare analyzes can be optimized using information on the actual luminance distributions of the surroundings. Currently, commercially available luminance distribution measurement devices are often not suitable for these kind of applications or simply too expensive for broad application. This paper describes the development of a practical and autonomous luminance distribution measurement device based on a credit card-sized single-board computer and a camera system. The luminance distribution was determined by capturing High Dynamic Range images and translating the RGB information to the CIE XYZ color space. The High Dynamic Range technology was essential to accurately capture the data needed to calculate the luminance distribution because it allows to capture luminance ranges occurring in real scenarios. The measurement results were represented in accordance with established methods in the field of daylighting. Measurements showed that the accuracy of the luminance distribution measurement device ranged from 5% to 20% (worst case) which was deemed acceptable for practical measurements and broad applications in the building realm.

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Al-Saleh, Jamal A., and Satish K. Agarwal. "Extended Beta Distribution and Mixture Distributions with applications to Bayesian analysis." Journal of Statistics Applications & Probability 2, no. 1 (March 1, 2013): 61–72. http://dx.doi.org/10.12785/jsap/020108.

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Volkmer, Hans, and G. G. Hamedani. "On distributions of order statistics and their applications to uniform distribution." Metrika 74, no. 2 (March 9, 2010): 287–95. http://dx.doi.org/10.1007/s00184-010-0303-y.

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50

R. Reis, Lucas David, Gauss M. Cordeiro, and Maria do Carmo S. Lima. "The Gamma-Chen distribution: a new family of distributions with applications." Spanish Journal of Statistics 2 (2021): 23–40. http://dx.doi.org/10.37830/sjs.2020.1.03.

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