Topp-Leone Mukherjee-Islam distribution: Properties and applications

In this paper, Topp-Leone Mukherjee-Islam (TLMI) distribution is suggested. The probability density function and the distribution function of the TLMI are provided. The rth moment, mean, variance, coefficient of skewness, kurtosis, and coefficient of variation are derived. The order statistics of the TLMI distribution random variable are introduced. Reliability analysis including the hazard rate function reliability function are studied. The maximum likelihood estimators of the TLMI distribution parameters and the R?nyi entropy as a measure of the uncertainty in the model are obtained. The usefulness of the TLMI distribution is illustrated using real lifetime data set from medical science.