In this article, a new three parameters lifetime model called the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution is introduced. Various properties of the model are derived, including moments, quantile function, survival function, hazard rate function, mean deviation and mode. The method of maximum likelihood is used to estimate the unknown parameters. The properties of the maximum likelihood estimators using Fisher information matrix are studied. Three real data sets are applied for illustrative purpose of this study.

In this article, the five-parameter beta Kumaraswamy exponential distribution (BKw-E) is introduced, and some characterizations of this distribution are obtained. The shape of the hazard function and some other important properties—such as median, mode, quantile function, and mean—are studied. In addition, the moments, skewness, and kurtosis are found. Furthermore, important measures such as Rényi entropy and order statistics are obtained; these have applications in many fields. An example of a real data set is discussed.

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.