Odd Inverse Power Generalized Weibull Generated Family of Distributions: Properties and Applications

A.S Al-Moisheer,Waleed Almutiry,I Elbatal,Mohammed Elgarhy,Lazim Abdullah

doi:10.1155/2021/5082192

Abstract

A novel family of produced distributions, odd inverse power generalized Weibull generated distributions, is introduced. Various mathematics structural properties for the odd inverse power generalized Weibull generated family are computed. Numerical analysis for mean, variance, skewness, and kurtosis is performed. The new family contains many new models, and the densities of the new models can be right skewed and symmetric with “unimodal” and “bimodal” shapes. Also, its hazard rate function can be “constant,” “decreasing,” “increasing,” “increasing-constant,” “upside-down-constant,” and “decreasing-constant.” Different types of entropies are calculated. Some numerical values of various entropies for some selected values of parameters for the odd inverse power generalized Weibull exponential model are computed. The maximum likelihood estimation, least square estimation, and weighted least square estimation approaches are used to estimate the OIPGW-G parameters. Many bivariate and multivariate type models have been also derived. Two real-world data sets are used to demonstrate the new family’s use and versatility.

Highlights

A novel family of produced distributions, odd inverse power generalized Weibull generated distributions, is introduced
Statisticians have been interested in proposing new families of univariate distributions that are derived from
Adding one or more form parameters results in these new generators, which improve accuracy and flexibility in modeling for a variety of diverse real-life applications. e most recent families of distributions to appear in the literature are as follows: a method for introducing a parameter into a family of distributions by [9], beta-G by [10], odd Nadarajah–Haghighi-G by [11], the odd Lindley-G by [12], and the odd Frechet-G by [13], odd generalized exponential-G by [14], exponentiated power generalized Weibull power series family of distributions by [15], and odd generalized NH-G by [16], among others

Summary

Important Representation

We give a helpful linear form for the OIPGW-G PDF . If |z1/z2| < 1 and ∇ > 0 is a real noninteger, the power series (PS) expansions hold. Where Πm+1(z) is the exp-G CDF with power parameter m + 1

Some Special Models of the OIPGW-G Family

Statistical Properties

Real Data Applications

Conclusions