Inference on the Parameters and Reliability Characteristics of Generalized Inverted Scale Family of Distributions based on Records

Ajit Chaturvedi,Ananya Malhotra

doi:10.19139/soic.v6i2.304

Abstract

A generalized inverted scale family of distributions is considered. Two measures of reliability are discussed, namely and . Point and interval estimation procedures are developed for the parameters, and based on records. Two types of point estimators are developed - uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES). A comparative study of different methods of estimation is done through simulation studies and asymptotic confidence intervals of the parameters based on MLE and log(MLE) are constructed. Testing procedures are also developed for the parametric functions of the distribution and a real life example has been analysed for illustrative purposes.

Highlights

A scale family of distributions plays an important role in reliability analysis with some of its most common members being exponential distribution, Rayleigh distribution, half-logistic distribution etc
Potdar and Shirke (2012, 2013) discussed inference on the scale family of lifetime distributions based on progressively censored data and generalized inverted scale family of distributions respectively
We develop uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) of the powers of the parameters and reliability functions of the generalized inverted scale family of distributions based on record data

Summary

Introduction

A scale family of distributions plays an important role in reliability analysis with some of its most common members being exponential distribution, Rayleigh distribution, half-logistic distribution etc. INFERENCE ON THE PARAMETERS AND RELIABILITY CHARACTERISTICS inferential procedures for ρ(t) and P for exponential distribution. Chaturvedi and Vyas (2017) developed estimation and testing procedures for the reliability functions of exponentiated distributions under Type I and Type II censoring. Several inferential procedures for the parameters of different distributions, based on record data, have been developed by Glick (1978), Nagaraja (1988a,1988b), Balakrishan et al (1995), Arnold et al (1992), Habibi et al (2006), Arashi and Emadi (2008), Razmkhah and Ahmadi (2011), Belaghi et al (2015) and others.

The Generalized Inverted Scale Family of Distributions

Point Estimation Procedures

Confidence Intervals

Testing of Hypotheses

Numerical Findings

Discussion