The Weibull Topp-Leone Generated Family of Distributions: Statistical Properties and Applications

Abstract

Statistical distributions are very useful in describing and predicting real world phenomena. Consequently, the choice of the most suitable statistical distribution for modeling given data is very important. In this paper, we propose a new class of lifetime distributions called the Weibull Topp-Leone Generated (WTLG) family. The proposed family is constructed via compounding the Weibull and the Topp-Leone distributions. It can provide better fits and is very flexible in comparison with the various known lifetime distributions. Several general statistical properties of the WTLG family are studied in details including density and hazard shapes, limit behavior, mixture representation, skewness and kurtosis, moments, moment generating function, incomplete moment. Different methods have been used to estimate its parameters. The performances of the estimators are numerically investigated. We have discussed inference on the new family based on the likelihood ratio statistics for testing some

A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

“…We shall compare thefits of the OBEE distribution with those of other competitive models [43] and Al-Babtain et al [3]. For comparing models, we consider the Cramér-Von Mises (C • ) and the Anderson-Darling (A • ) and the Kolmogorov-Smirnov (KS) statistic.…”

A Novel Two-Parameter Compound G Family of Probability Distributions With Some Copulas, Statistical Properties and Applications

“…In the last few years, huge efforts have been paid to derive many new G families using the well knowm methods. These new G families have been used for modeling non-censored and censored real data sets in many applied studies such as finance, econometrics, value at risk applications, insurance, biology, engineering, forecasting, medicine and environmental sciences see , for example, Marshall and Olkin [48] (Marshall-Olkin-G (MO-G) family), Eugene et al [19] (beta generalized-G (B-G) family), Yousof et al [68] (transmuted exponentiated generalized (TEG) family), Rezaei et al [57] (Topp Leone generated (TLG) family), Merovci et al [50] (exponentiated transmuted-G (ET-G) family), Aryal and Yousof [13] (exponentiated generalized-G Poisson (EGGP) family), Brito et al [14] (Topp-Leone odd log-logistic-G (TLOLL-G) family), Yousof et al [70] (Burr of the type X G (BX-G) family), Hamedani et al [30] (type I general exponential-G (TIGE-G) family), Korkmaz et al [40] (exponential Lindley odd log-logistic-G (ELOLL-G) family), Cordeiro et al (2018) (Burr XII-G (BXII-G) family), Hamedani et al [28] (extended-G (Ex-G) family), Korkmaz et al [41] (Marshall-Olkin generalized-G Poisson (MOGGP) family), Yousof et al [73] (Burr-Hatke-G (BH-G) family), Nascimento et al [55] (Nadarajah-Haghighi-G (NH-G) family), Hamedani et al [29] ( type II general exponential-G (TIIGE-G) family), Yousof et al [75] (Weibull G Poisson (WGP) family), Merovci et al [51] (Poisson Topp Leone G (PTL-G) family), Karamikabir et al [38] (Weibull Topp-Leone generated (WTL-G) family), Korkmaz et al [39] (Hjorth-G (Hj-G) family), 346 TWO-PARAMETER COMPOUND G FAMILY OF PROBABILITY DISTRIBUTIONS Alizadeh et al [9] (flexible Weibull generated (FWG) family) and Alizadeh et al [10] (transmuted odd log-logistic-G (TOLL-G) family), El-Morshedy et al [22] (Poisson generalized exponential G (PGE-G) family) among others.…”

A New Family of Continuous Distributions: Properties, Copulas and Real Life Data Modeling

“…Recently, many statisticians have focused on the more complex and flexible continuous probability distributions for increasing the applicable ability of these well-known models via adding one or more shape parameters. The well-known family of distributions can be cited as follows: Marshall and Olkin [42] (Marshall and Olkin family), Zografos and Balakrishnan [63] (gamma family), Cordeiro and de Castro [13] (Kumaraswamy family), Yousof et al [57] (Burr type X family), Cordeiro et al [12] (Burr type XII family), Merovci et al [43] (exponentiated transmuted family), Aryal and Yousof [8] (exponentiated generalized-G Poisson family), Brito et al [10] (Topp-Leone odd log-logistic family), Korkmaz et al [33] (generalized odd Weibull generated family), Korkmaz et al [35] (exponential Lindley odd log-logistic family), Korkmaz et al [36] (Marshall-Olkin generalized-G Poisson family), Nascimento et al [46] (Nadarajah-Haghighi family), Merovci et al [44] (Poisson Topp Leone family), Karamikabir et al [32] (Weibull 749 Topp-Leone generated family), Korkmaz et al [34] (Hjorth family), Alizadeh et al [4] (flexible Weibull generated family), Alizadeh et al [5] (transmuted odd log-logistic family) and El-Morshedy et al [16] (Poisson generalized exponential family)…”