The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.
This paper considers and studies a distinct special case of omega distribution defined on the unit interval [Formula: see text], called unit-omega distribution. Thanks to its simple form, some of its basic properties are derived. The maximum likelihood method, Bayes method, and the method of moments are used to estimate the parameters of unit-omega distribution. These estimation methods are examined by conducting a simulation study. More importantly, the quantile function of unit-omega distribution has a closed-form expression that allows modeling the conditional quantiles of a unit response variable as a function of covariates. Residual analysis is performed using randomized quantile residuals and Cox–Snell residuals. The proposed approach is used to model the quantiles of child mortality rates, conditional on covariates. These covariates represent the proportions of people left behind across three key indicators: nutrition, availability of safe drinking sources and adequate education. Another application that relates to recovery rates of viable CD34+ cell is presented. From both applications, the fitting results of the proposed regression model outperform those of beta, Kumaraswamy and unit-Weibull regression models.
New classes of continuous distributions have been generated, in the last decad, based on a compounding procedure arises on a latent competing risks problem. This procedure assumes the homogeneity between the population individuals. In this paper, a new lifetime distribution is generated, assuming the heterogeneity at both population and individual levels, called Extended Gamma Gompertz (EGG) distribution. This distribution shows very desirable exibility of its hazard function. Some properties of the proposed distribution are given. Maximum likelihood estimation technique is used to estimate the parameters. A simulation study is performed to examine the performance of the proposed model. Finally, application to a real data set is given to exemplify the utility of the EGG distribution.
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