A Novel Two-parameter Nadarajah-Haghighi Extension: Properties, Copulas, Modeling Real Data and Different Estimation Methods

A new two-parameter lifetime distribution is proposed and numerically studied. The new model has a flflexible failure rate shapes such as “monotonically increasing” , “monotonically decreasing” , “bathtub” , “constant” , “upside down” and “J-shape” . Various of its statistical properties are derived. A numerical analysis of skewness and kurtosis are presented. Many bivariate and multivariate extensions are also presented via Farlie Gumbel Morgenstern copula, Renyi entropy copula, modifified Farlie Gumbel Morgenstern copula and Clayton copula. Several estimation methods such as the maximum likelihood, Cramer-von-Mises, L-moment estimation, Anderson Darling, right Tail-Anderson Darling estimation and left tail-Anderson Darling are presented and considered. Numerical simulations are performed to assess the performance of estimation methods. An environmental data set is employed to measure flflexibility of the new model also to compare the estimation methods.