A New Generalization of Quadratic Hazard Rate Distribution

Ibrahim Elbatal,Nadeem Shafique Butt

doi:10.18187/pjsor.v9i4.678

Abstract

For the first time, a five-parameter distribution, called the kumaraswamy quadratic hazard rate distribution is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the Linear failure rate, Exponential and Rayleigh distributions, among several others. We obtain the moments, moment generating and quantile functions. We discuss the method of maximum likelihood to estimate the model parameters and determine the observed information matrix. A real data sets illustrate the importance and flexibility of the proposed models. Normal 0 false false false EN-US X-NONE AR-SA

Highlights

The quadratic hazard rate distribution (QHR) distribution was introduced by Bain (1974)
To derive some mathematical properties of a new model, called the Kumaraswamy quadratic hazard rate (KQHR) distribution, which stems from the following general construction: if G
The reliability function (RF) of the Kumaraswamy quadratic hazard rate distribution is denoted by RKQHR (x) known as the survivor function and is defined as

Summary

Introduction

The quadratic hazard rate distribution (QHR) distribution was introduced by Bain (1974). The QHRD may have an increasing (decreasing) hazard function or a bathtub shaped hazard function or an upsidedown bathtub shaped hazard function This property enables this distribution to be used in many applications in several areas, such as reliability, life testing, survival analysis and others. A random variable X is said to have the quadratic hazard rate distribution (QHRD) with three parameters , , and , if it has the cumulative distribution function ( x x2 x3) G(x, , , ) = 1 e 2 3 , x > 0,. To derive some mathematical properties of a new model, called the Kumaraswamy quadratic hazard rate (KQHR) distribution, which stems from the following general construction: if G denotes the baseline cumulative function of a random variable, a generalized class of distributions can be defined by FX |(a,b) (x) = 1 1 G(x)a b (1.5).

P X11 x a b

Kumaraswamy Quadratic Hazard Rate Distribution

Reliability Analysis

Statistical Properties

Moment Generating Function

Order Statistics

Least Squares and Weighted Least Squares Estimators

Maximum Likelihood Estimators

Application