Gamma-exponential Distribution (GED): Theory and Its Properties
Ajewole K. P. *
Department of Physical Sciences, Mathematics Programme, Landmark University, Omu-Aran, Nigeria.
Ogunwale O. D.
Department of Statistics, Ekiti State University, Ado-Ekiti, Nigeria.
Ilesanmi A. O.
Department of Statistics, Ekiti State University, Ado-Ekiti, Nigeria.
Odukoya E. A.
Department of Statistics, Ekiti State University, Ado-Ekiti, Nigeria.
Olayinka K. P.
Department of Statistics, Ekiti State University, Ado-Ekiti, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Research on probability distribution functions and their characteristics is necessary, even though these functions are essential for modeling random processes. Studies have shown, however, that in some circumstances, it is found that specific combinations of two or more random variables with known probability distributions follow the distributions of some real-world data that the currently used standard distributions are unable to adequately represent.
This study concentrated on developing the two-parameter Gamma-Exponential Distribution (GED), which was achieved by applying the Transformed-Transformer method, in order to produce a new distribution that combines the gamma and exponential distributions. Expressions for its survival and hazard functions, as well as the probability density function, cumulative distribution function, rth non-central moments, first four moments, variances, skewness and kurtosis and maximum likelihood estimator were among its attributes.
Keywords: Probability distribution, Gamma-x family, gamma-exponential distribution, maximum likelihood estimator, survival function