A Novel Two-Parameter Compound G Family of Probability Distributions With Some Copulas, Statistical Properties and Applications

Abstract

In this work, we introduce a new G family with two-parameter called the compound reversed Rayleigh-G family. Several relevant mathematical and statistical properties are derived and analyzed. The new density can be heavy tail and right skewed with one peak, symmetric density, simple right skewed density with one peak, asymmetric right skewed with one peak and a heavy tail and right skewed with no peak. The new hazard function can be "upsidedown-constant", "constant", "increasing-constant", "revised J shape", "upside-down", "J shape" and "increasing". Many bivariate types have been also derived via di¤erent common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and ‡exibility of the new family is illustrated by means of two real data sets.