Statistical Analysis of Joint Progressive Censoring Data from Gompertz Distribution

In this paper, we consider the problems of estimating the unknown parameters as well as predicting the failure times of the removed units in multiple stages of the joint progressively censored sample coming from two Gompertz distributions. The likelihood, Bootstrap and Bayesian methods are applied for the estimation problem. In Bayesian contexts, the posterior densities are estimated by using Lindley’s approximation, importance sampling and Metropolis-Hastings methods under different loss error functions. The confidence intervals based on the asymptotic normality and credible intervals based the Bayesian approach are discussed as well. A real life data is analyzed for illustrative purposes and Monte Carlo simulations are conducted to compare the performances of the all proposed methods

Record data from Kies distribution and related statistical inferences

The Kies probability model was proposed as an alternative to the extendedWeibull models as it provides a more efficient fit to some real-life data sets in comparison to the aforementioned models. The paper proposes classical and Bayesian inferences for the Kies distribution based on records. Maximum likelihood estimates are studied jointly with asymptotic and bootstrap confidence intervals. Moreover, Bayes estimates, along with credible intervals are discussed assuming squared and LINEX loss functions. The proposed estimation methods have been investigated and compared via simulation studies. A real data set has been analysed for illustrative purposes

Tail-adaptive location rank test for the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) was recently introduced as a modeling tool in data analysis. The GSHD is a unimodal distribution that is completely specified by location, scale, and shape parameters. It has also been shown elsewhere that the rank procedures of location are regular, robust, and asymptotically fully efficient. In this article, we study certain tail weight measures for the GSHD and introduce a tail-adaptive rank procedure of location based on those tail weight measures. We investigate the properties of the new adaptive rank procedure and compare it to some conventional estimators