THE INVERSE BURR LOG-LOGISTIC DISTRIBUTION: PROPERTIES, APPLICATIONS AND DIFFERENT METHODS OF ESTIMATION

Lifetime distributions have played a significant role in lifetime data analysis. Despite the numerous distributions in literature, there have been several motivations for developing new ones. In this paper, a new lifetime distribution is proposed. Some important functions of the new distribution, such as probability density, cumulative distribution, survival, hazard, and quantile are derived in closed form. Some distributional properties such as moments, moment generating function, linear representation, probability weighted moments, etc. are obtained. Some estimators such as the least square estimator (LSE), the weighted least square estimator (WLSE), the Anderson-Darling estimator (ADE) and the Cramer-von Mises estimator (CvME) are investigated for three unknown parameters. The efficiency of the estimators is checked via Monte Carlo simulation based on the bias and mean square error criteria. The usability of the new distribution is investigated with two real data sets and empirical results obtained reveal that the new distribution offers a promising fit for the data sets under study.