A New Extended-F Family: Properties and Applications to Lifetime Data

Saima K Khosa,Saddam Hussain,Zubair Ahmad,Mi Zichuan,Ahmed Z Afify,Anum Iftikhar

doi:10.1155/2020/5498638

Abstract

In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as a special submodel of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived, and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data, and the comparison is made with the Weibull and some of its well-known extensions such as Marshall–Olkin Weibull, alpha power-transformed Weibull, and Kumaraswamy Weibull distributions.

Highlights

In many practical situations, classical distributions do not provide adequate fits to real data
We further propose a new method to provide flexible lifetime distributions called a new extendedF (NE-F)family with additional shape parameter θ. e proposed NE-F family is specified by the following cdf: G(x; θ, ξ) F(x; ξ)eθF(x;ξ), θ, ξ > 0, x ∈ R, (3)
E key motivations for using the NE-F family of distributions in practice are as follows: (i) A very simple and convenient method of adding an additional parameter to modify the existing distributions (ii) To improve the characteristics and flexibility of the existing distributions (iii) To introduce the extended version of the baseline distribution whose cdf, survival function, and hrf have closed forms (iv) To compare the goodness of fit with other wellknown models having the same, as well as higher, number of parameters (v) To provide better fits than the other competing modified models is paper is unfolded as follows

Summary

Introduction

Classical distributions do not provide adequate fits to real data. Is has been performed via extending the classical distributions by introducing additional parameter(s) to the baseline model. We further propose a new method to provide flexible lifetime distributions called a new extendedF (NE-F)family with additional shape parameter θ. (i) A very simple and convenient method of adding an additional parameter to modify the existing distributions (ii) To improve the characteristics and flexibility of the existing distributions (iii) To introduce the extended version of the baseline distribution whose cdf, survival function (sf ), and hrf have closed forms (iv) To compare the goodness of fit with other wellknown models having the same, as well as higher, number of parameters (v) To provide better fits than the other competing modified models is paper is unfolded as follows. Plots for the pdf and hrf of the NE-W for selected parametric values are shown in Figures 1 and 2, respectively

Properties of the NE-F Family

The NE-W Distribution

Data 1

Data 2