Survival analysis of random censoring with inverse Maxwell distribution: an application to guinea pigs data

In real-life situations, performing an experiment up to a certain period of time or getting the desired number of failures is time-consuming and costly. Many of the available observations remain censored and only give the survival information of testing units up to a noted time and not about the exact failure times. In this article, the inverse Maxwell distribution having an upside-down hazard rate is considered a survival lifetime model. The censoring time is also assumed to follow the inverse Maxwell distribution with a different parameter. The probability of failure of an item before censoring and expected and observed time on the test is derived from a random censoring scheme. The maximum likelihood estimators with their confidence intervals for the parameters are obtained for a randomly censored setup. The Bayes estimators are also obtained by taking the inverted gamma distribution as a prior under squared error loss function. In Bayesian analysis, the two techniques i.e. Markov Chain Monte Carlo and Tierney-Kadane approximation methods are used for estimation purposes. For checking the performances of proposed estimators, we performed an extensive simulation study. A real data, guinea pigs, is analyzed to support the proposed study.