A New Flexible Three-Parameter Compound Chen Distribution: Properties, Copula and Modeling Relief Times and Minimum Flow Data

In this work, a new flexible extension of the Chen distribution is derived and studied. The new density accommodates the "unimodal right skewed", "unimodal left skewed", "bimodal right skewed" and "bimodal left skewed" shapes. The new hazard rate can be "decreasing-constant-increasing (bathtub)", "monotonically increasing", "upside down constant-increasing", "monotonically decreasing", "upside down" and "J shape". Some of its statistical properties such as moments, mean residual lifetime, conditional moments and mean past lifetime are derived. Some bivariate extensions using Ali-Mikhail-Haq copula, Renyi copula, Farlie-Gumbel-Morgenstern, Clayton copula and modified Farlie-Gumbel-Morgenstern copula are derived. Two real data sets are analyzed for illustrating the wide applicability of the new model. The new model is compared with many common competitive models under some well-known goodness-of-fit statistic criteria.