The Odd Moment Exponential Family of Distributions: Its Properties and Applications

A new family of continuous distributions called Odd Moment exponential-G family of distributions is proposed. The density and cumulative distribution function are expressed as linear infinite mixtures of exponentiated-G family of the baseline distribution. Some mathematical properties of this new family such as skewness and kurtosis, asymptotes, shapes, moment generating function, distribution of order statistics and power moments are investigated. The model parameter estimation by employing the method of maximum likelihood is discussed. To check the suitability, the proposed model is compared to its submodels and also with useful lifetime models namely the gamma, exponentiated exponential, exponentiated moment exponential and beta exponential distributions by conducting three data fitting experiments with real-life data sets.