Mathematical Properties of the Inverted Topp-Leone Family of Distributions

Source abstract

This article defines an inverted Topp-Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability $R$, moments, R\'enyi entropy, Shannon entropy, Fisher information matrix, partial ordering associated with this distribution have been derived. Distributions of sum and quotient of two independent inverted Topp-Leone variables have also been obtained.