On Extended Generalized Exponential Distribution

In this paper, we present a generalized exponential distribution that contains four parameters. This distribution further generalizes previously established generalized exponential distributions which now serves as special cases of the new four-parameter generalized exponential distribution. The properties of the new distribution like the cumulative distribution function, the survival function, the hazard function, the moment generating function, the median, the 100p-percentile point and the mode of distribution are established. The moment function of the distribution which cannot be obtained in close form is numerically obtained and tabulated for some selected values of the parameters. A Theorem that characterized the distribution is stated and proved.