A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

Abstract

In this paper, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index is performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "decreasing", "increasing", "increasing-constant", "upside down-constant", "decreasing nstant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The usefulness and flexibility of the new distribution is illustrated by means of two real data sets.

Partial Bayes Estimation of Two Parameter Gamma Distribution Under Non-Informative Prior

“…In order to compare the fits of the distributions, we consider Cramèr-Von-Mises (CVM) and Anderson-Darling (AD) goodness of fit statistics. These two statistics are essentially modifications of the K-S test statistic and are usually thought to be more powerful than the original K-S test, which are also favoured by many researchers (for example Yousof et al [32], Ibrahim et al [30], Khalil et al [26], Lak et al [27], Elgohari [29], Mohamed et al [28]). Moreover for more accuracy, we consider another five goodness of fit measures based on the log-likelihood functions namely, -2 × log-likelihood (-2logL), Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Hannan-Quinn Information Criterion (HQIC), Bayesian Information Criterion (BIC).…”