A new extended generalized Gompertz distribution with statistical properties and simulations

Statistical distributions are very useful in describing and predicting real world phenomena. In many applied areas there is a clear need for the extended forms of the well-known distributions. Generally, the new distributions are more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the best-suited statistical distribution for modeling data is very important.In this article, we proposed an extended generalized Gompertz (EGGo) family of EGGo. Certain statistical properties of EGGo family including distribution shapes, hazard function, skewness, limit behavior, moments and order statistics are discussed. The flexibility of this family is assessed by its application to real data sets and comparison with other competing distributions. The maximum likelihood equations for estimating the parameters based on real data are given. The performances of the estimators such as maximum likelihood estimators, least squares estimators, weighted least squares estimators, Cramer-von-Mises estimators, Anderson-Darling estimators and right tailed Anderson-Darling estimators are discussed. The likelihood ratio test is derived to illustrate that the EGGo distribution is better than other nested models in fitting data set or not. We use R software for simulation in order to perform applications and test the validity of this model.