Some Characterizations of Log‐Cauchy Distribution and Its Inferential Exploration Under Progressive First‐Failure Censoring Scheme

ABSTRACT The meteoric developments of cutting‐edge technologies in the modern era expedited the advancements of infrastructure in the industrial and biomedical sectors. As a result, the lifetimes of products or patients have considerably increased. In practice, lifetime data are usually modeled with a probability distribution to capture the inherent randomness in the data. When life‐testing experiments produce data containing extreme observations, resorting to heavy‐tailed distributions is often an immediate choice for the researchers. In this paper, log‐Cauchy, a super‐heavy‐tailed distribution, is explored as a lifetime model in the context of analyzing survival and reliability data, and some characterizations of this lifetime distribution are discussed. Further, the considered distribution is examined under a progressive first‐failure type‐II censoring, a technique known for reducing the test completion time when products are highly reliable. Apart from the maximum likelihood estimators, the Bayes estimators of the distribution parameters with dependent priors under a symmetric loss function are investigated under the considered censoring scheme. The estimators of the reliability and hazard functions have also been obtained in this study. Moreover, a quantile‐based measure of experiment completion time has been discussed. The performance of the estimators and the behavior of the experiment completion time have been evaluated through a Monte Carlo study. Additionally, a prediction technique has been developed to predict the potential lifetimes of the censored units. Finally, a reliability and survival data set has been used to illustrate the real‐life applicability of the proposed distribution and the associated procedures.