Statistical Properties of a Generalization Erlang Truncated Exponential Distribution with Applications and Its Bivariate Extension

Using power exponentiated family, this paper introduces the New Power Exponentiated Erlang-Truncated Exponential distribution as a new generalization of the Erlang-Truncated Exponential distribution. The suggested distribution has constant and increasing shapes for hazard rate function. Numerous structural characteristics are derived, including quantile function, moments, moment generating function, behavior of hazard, reversed hazard and cumulative hazard functions, entropy measures, stochastic ordering, and order statistics. The model parameters are estimated by maximum likelihood, Cramer von Mises, and Percentiles estimation methods. A numerical study is performed using simulated data to examine performance of the different estimators with varying sample size. The flexibility and potentiality of proposed model and some existing models are examined using two actual data sets and some criteria for model selection and goodness of fit test statistics. Finally, a bivariate extension of the suggested distribution called the bivariate new power exponentiated erlang-truncated exponential distribution was introduced. The recommended bivariate distribution is of type Farlie--Gumbel--Morgenstern copula. The proposed distribution has joint probability density function, the joint cumulative function, and joint survival function. In addition, Some statistical properties of the distribution are also obtained.