Inference under progressively type II right censored sampling for certain lifetime distributions

In this paper, estimation of the parameters of a certain family of two-parameter lifetime distributions based on progressively Type II right censored samples (including ordinary Type II right censoring) is studied. This family, of reverse hazard distributions, includes the Weibull, Gompertz and Lomax distributions. A new type of parameter estimation, named inverse estimation, is introduced for both parameters. Exact confidence intervals for one of the parameters and generalized confidence intervals for the other are explored; inference for the first parameter can be accomplished by our methodology independently of the unknown value of the other parameter in this family of distributions. Derivation of the estimation method uses properties of order statistics. A simulation study in the particular context of the Weibull distribution illustrates the accuracy of these confidence intervals and compares inverse estimators favorably with maximum likelihood estimators. A numerical example is used to illustrate the proposed procedures

On stochastic comparisons of largest order statistics in the scale model

Let $X_{\lambda _{1}},X_{\lambda _{2}},\ldots ,X_{\lambda _{n}}$ be independent nonnegative random variables with $X_{\lambda _{i}}\sim F(\lambda _{i}t)$, $i=1,\ldots ,n$, where $\lambda _{i}>0$, $i=1,\ldots ,n$ and $F$ is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic $X_{n:n}^{\lambda }$ is smaller than another one $X_{n:n}^{\theta }$ according to likelihood ratio ordering. Furthermore, we apply these results when $F$ is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases

Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring

The hybrid censoring is a mixture of Type I and Type II censoring schemes. This paper presents the statistical inferences of the Inverse Weibull distribution when the data are Type-I hybrid censored. First we consider the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators can not be obtained in closed form. We further obtain the Bayes estimators and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimators using Lindley's approximation technique. We have performed a simulation study and a real data analysis in order to compare the proposed Bayes estimators with the maximum likelihood estimators.Comment: This paper is under review in the Austrian Journal of Statistics and will likely be published ther