A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family

Abstract

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions.

Inference of Inverted Exponentiated Lomax Distribution based on Step-Stress Partially Accelerated Life Test under Progressive Type II Censoring

“…This section examines two genuine data sets, the first of which was researched and presented by Hassan and Mohamed (2019) and the second of which was researched and presented by Klakattawi et al (2022). The IEL better distribution, however (see Hassan and Mohamed (2019)), is consistent with the smaller values of the earlier measures.…”

Harmonic Mixture Weibull-G Family of Distributions: Properties, Regression and Applications to Medical Data

“…Consequently, new families of distributions in the form of extended or modified versions of the Weibull distribution have been introduced in literature with the attempt of increasing its flexibility. Some examples include the following: Marshall-Olkin Weibull generated family [2], exponentiated power generalized Weibull power series family of distributions [3], complementary generalized power Weibull power series family of distributions [4], the Burr-Weibull power series family [5], extended Weibull-G family [6], Weibull Burr X-G family of distributions [7], the Weibull Marshall-Olkin family [8], the gamma-Weibull-G family [9], generalized odd Weibull generated family [10], the beta Weibull-G family [11], Kumaraswamy Weibullgenerated family [12], generalized extended Weibull power series family of distributions [13], the inverse Weibull power series family [14], the Marshall-Olkin extended Weibull family of distributions, [15] and the extended Weibull power series family [16].…”

A New Flexible Logarithmic‐X Family of Distributions with Applications to Biological Systems

“…In the past decade, researchers' efforts have been devoted to deriving new families of probability distributions. e new probability distributions have been constructed by adding one or more new additional parameters to the baseline models (El-Morshedy et al [8]; Guerra et al [9]; Reyad et al [10]; Bantan et al [11]; Eghwerido et al [12]; Eghwerido and Agu [13]; Alzaatreh et al [14]; Lahcene [15]; ElSherpieny and Almetwally [16]; Roozegar et al [17]; Klakattawi et al [18]; Hussein et al [19]; and Kilai et al [20]).…”