Type II Topp Leone Generalized Inverted Exponential Distribution with Real Data Applications
Zakeia A. Al-Saiary *
Department of Statistics, College of Science, University of Jeddah, Jeddah 22254, Saudi Arabia.
Sarah H. Al-Jadaani
Department of Statistics, College of Science, University of Jeddah, Jeddah 22254, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
The generalization of standard and generalized distributions has become one of the concerns that the statistical theory depends on to obtain more exible distributions. In this article, a new distribution that is considered a generalization of the generalized inverted exponential distribution called the Type II Topp Leone Generalized Inverted Exponential (TIITLGIE) distribution is introduced. Some statistical properties of this distribution were obtained. The quantile function, median, moments, moment generating function, Reliability function, hazard function, mode, harmonic mean, mean and median deviation are derived. Furthermore, important measures such Rnyi entropy and the Maximum Likelihood (ML) estimation are deduced for parameters. Conduct a Monte Carlo simulation to study behavior of parameter estimates. Finally, applications on three real data sets are discussed.
Keywords: Generalized inverted exponential distribution, Type II Tope Leone, Rnyi entropy, maximum likelihood estimation, Monte Carlo simulation