The Half-Logistic Generalized Weibull Distribution

Masood Anwar,Amna Bibi

doi:10.1155/2018/8767826

Abstract

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

Highlights

Statistical distributions are the basic aspects of all parametric statistical techniques including inference, modeling, survival analysis, and reliability
We propose the half-logistic generalized Weibull (HLGW) distribution without adding any extra parameter to the baseline model
There is no difference between HLGW and Weibull distribution based on the likelihood ratio (LR) test; the goodness-of-fit statistics W∗, A∗, and K-S statistic clearly show that HLGW distribution is better than Weibull distribution for the data

Summary

Introduction

Statistical distributions are the basic aspects of all parametric statistical techniques including inference, modeling, survival analysis, and reliability. Marshall and Olkin [2] introduced an effective technique to extend a family of distributions by addition of another parameter By applying this technique, they generalized the exponential and the Weibull distributions. Nadarajah and Kotz [7], Lai et al [8], Lai et al [9], and Xie et al [10] further discussed some modifications of the Weibull model In this paper, another extension of the extended Weibull distribution is introduced using half-logistic-G generator. We propose the half-logistic generalized Weibull (HLGW) distribution without adding any extra parameter to the baseline model. A three-parameter lifetime model is presented which is the compound model of the previously known models introduced by Dimitrakopoulou et al [11] and half-logistic-G (HL-G) distribution called half-logistic generalized Weibull (HLGW) distribution.

The Half-Logistic Generalized Weibull Distribution

Distributional Properties

Estimation

Simulation Study

Applications

Conclusion