On cumulative residual Kullback–Leibler information

Aging Intensity for Step-Stress Accelerated Life Testing Experiments

The aging intensity (AI), defined as the ratio of the instantaneous hazard rate and a baseline hazard rate, is a useful tool for the describing reliability properties of a random variable corresponding to a lifetime. In this work, the concept of AI is introduced in step-stress accelerated life testing (SSALT) experiments, providing new insights to the model and enabling the further clarification of the differences between the two commonly employed cumulative exposure (CE) and tampered failure rate (TFR) models. New AI-based estimators for the parameters of a SSALT model are proposed and compared to the MLEs in terms of examples and a simulation study.

Elaboration Models with Symmetric Information Divergence

Various statistical methodologies embed a probability distribution in a more flexible family of distributions. The latter is called elaboration model, which is constructed by choice or a formal procedure and evaluated by asymmetric measures such as the likelihood ratio and Kullback-Leibler information. The use of asymmetric measures can be problematic for this purpose. This paper introduces two formal procedures, referred to as link functions, that embed any baseline distribution with a continuous density on the real line into model elaborations. Conditions are given for the link functions to render symmetric Kullback-Leibler divergence, Rényi divergence, and phi-divergence family. The first link function elaborates quantiles of the baseline probability distribution. This approach produces continuous counterparts of the binary probability models. Examples include the Cauchy, probit, logit, Laplace, and Student-t links. The second link function elaborates the baseline survival function. Examples include the proportional odds and change point links. The logistic distribution is characterized as the one that satisfies the conditions for both links. An application demonstrates advantages of symmetric divergence measures for assessing the efficacy of covariates.

Goodness of Fit Tests for the Log-Logistic Distribution Based on Cumulative Entropy under Progressive Type II Censoring

In this paper, we propose two new methods to perform goodness-of-fit tests on the log-logistic distribution under progressive Type II censoring based on the cumulative residual Kullback-Leibler information and cumulative Kullback-Leibler information. Maximum likelihood estimation and the EM algorithm are used for statistical inference of the unknown parameter. The Monte Carlo simulation is conducted to study the power analysis on the alternative distributions of the hazard function monotonically increasing and decreasing. Finally, we present illustrative examples to show the applicability of the proposed methods.