Nadarajah exponential distribution. He derived the expressionsNadarajah exponential distribution. He derived the expressions

Nadarajah 87 provided a comprehensive survey of the mathematical properties of the exponentiated exponential distribution. He derived the expressions for the moment generating function, characteristic function, cumulant generating function, the nth moment, the first four moments, variance, skewness, kurtosis, the nth conditional moment, the first four cumulants, mean deviation about the mean, mean deviation about the median, Bonferroni curve, Lorenz curve, Bonferroni concentration index, Gini concentration index, Rényi entropy, Shannon entropy, cumulative residual entropy, Song’s measure, moments of order statistics, L moments, asymptotic distribution of the extreme order statistics, reliability, distribution of the sum of exponentiated exponential random variables, distribution of the product of exponentiated exponential random variables and the distribution of the ratio of exponentiated exponential random variables. He also discussed estimation by the method of maximum likelihood, including the case of censoring, and provide simpler expressions for the Fisher information matrix.                Kundu and Gupta 27, in a larger class of distributions attained by introducing another shape parameter to the two-parameter generalized exponential distribution. Because of the additional shape parameter, more flexibility had been introduced in the family. It was observed that the new family is positively skewed, and has increasing, decreasing, unimodal and bathtub-shaped hazard functions. It can be observed as a proportional reversed hazard family of distributions. This new family of distributions was analytically quite tractable and it can be used quite effectively to analyze censored data also. Analysis of two data sets are performed and the results are quite satisfactory.               Saralees Nadarajah and Firoozeh Haghighi 88 was presented a generalization of the exponential distribution. The generalization always has its mode at zero and yet allows for increasing, decreasing and constant hazard rates. It can be used as an alternative to the gamma, Weibull, and exponentiated exponential distributions. A comprehensive account of the mathematical properties of the generalization was presented. A real data example was discussed to illustrate its applicability.               Based on generalized order statistics, Eldesoky E Afify 32 were obtained the estimation of a parameter of generalized exponential distribution by. The maximum likelihood and Bayes methods were used by them for this purpose. Survival function and hazard rate were also computed. Estimation based on upper record values from generalized exponential distribution was obtained as a special case and compared by simulated data.                Lemonte Artur 75 was introduced a new three-parameter exponential-type family of distributions which can be used in modeling survival data, reliability problems and fatigue life studies. Its failure rate function can be constant, decreasing, increasing, upside-down bathtub or bathtub-shape depending on its parameters. It includes as special sub-models the exponential distribution, the generalized exponential distribution (Gupta and Kundu 53) and the extended exponential distribution (Nadarajah and Haghighi 88). He was provided a comprehensive account of the mathematical properties of the new family of distributions. Maximum likelihood estimation of the unknown parameters of the new model for the complete sample as well as for censored sample was discussed. Estimation of the stress–strength parameter was also considered. He presented two empirical applications of the new model to real data for illustrative purposes.               Lemonte Artur et al. 76 proposed a generalization of the Kumaraswamy distribution referred to as the exponentiated Kumaraswamy distribution and its log-transform. They also discussed the moments, moment generating function, mean deviations, Bonferroni and Lorentz curves, the density of the order statistics and their moments and maximum likelihood estimation of the model parameters.               Jailson De Araujo Rodrigues and Ana Paula Coelho Madeira Silva 59 was introduced a new continuous distribution known as exponentiated Kumaraswamy-exponential that extends the exponential distribution and some other distributions. Several structural properties of the new distribution were investigated, including the moments, hazard function, mean deviation and Re´nyi entropy. Moreover, they have discussed the maximum likelihood estimation of this distribution and give an application reveals that the model proposed can be very useful in fitting real data.