Abstract
In this study, we have considered the proportional hazard version of the inverse Weibull distribution. It has been shown that the density and hazard rate functions are unimodal and the mean residual life function is bathtub shaped. For the considered model, many functions of the parameters, such as the mean, variance, coefficient of variation and the critical points of the density, hazard rate and mean residual life functions cannot be given in explicit form. As a result, the variances of the maximum likelihood estimators of such functions cannot be given in explicit form to construct the usual asymptotic confidence interval. In this study, we use the percentile bootstrap estimation method to estimate such variances to construct the asymptotic confidence intervals. The asymptotic confidence intervals are compared with the bootstrap confidence intervals. Simulation studies are carried out to examine the performance of the maximum likelihood and bootstrap estimators. An example is provided to illustrate the procedure.
Highlights
The proportional hazard model has been widely used to analyze survival data
Let Y be a random variable with survival function S1(y) and hazard srautrevivfualncftuinocntioλn1(yS)(.x)T=he[nS1(ax)]rαa,nαdo>m0, variable X with has proportional hazard rate function λ(x) = αλ1(x)
The main purpose of this paper is to study the bootstrap estimation of the parameters of the Proportional hazard Inverse Weibull (PHIW) distribution and the associated functions including the mean, variance, coefficient of variation, the probability density, the hazard rate and mean residual life functions
Summary
The proportional hazard model has been widely used to analyze survival data. let Y be a random variable with survival function S1(y) and hazard srautrevivfualncftuinocntioλn1(yS)(.x)T=he[nS1(ax)]rαa,nαdo>m0, variable X with has proportional hazard rate function λ(x) = αλ1(x). We are interested in the Proportional hazard Inverse Weibull (PHIW) distribution with survival function given by ( ) S ( x) = 1 − e−λx−β α , x > 0, α , β ,λ > 0. It may be noted that analogues to the proportional hazard model, the proportional reversed hazard rate model has been studied in the literature In this case, the power of the distribution function is considered instead of the power of the survival function. The main purpose of this paper is to study the bootstrap estimation of the parameters of the PHIW distribution and the associated functions including the mean, variance, coefficient of variation, the probability density, the hazard rate and mean residual life functions.
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