In this paper the T-R{Y} framework is used for proposing a new distribution that called The Lomax-Gumbel{Frechet} distribution. We study in details the properties of this distribution including hazard function, quantile Function, the skewness, the kurtosis, transformation, Renyi entropy, and moment generating function. Estimate of the parameters will be obtained using the MLE method. We present a simulation study and t the distribution to two real data sets.

In this article, we introduce a Bayesian analysis for the Kumaraswamy-Weibull (Kum-W) distribution. Approximate Bayes estimates are obtained under the assumptions of non-informative priors using the Gibbs sampling procedure. This procedure allows for generating samples from posterior distributions. Also, using Bayesian framework, the predictive density for a single future response, a bivariate future response, and several future responses are derived. The predictive means, standard deviations, highest predictive density (HPD) intervals, and the shape characteristics for a single future response are determined. Finally, applications to real data sets are utilized to illustrate the potentiality of the Bayesian analysis and the predictive results.

The Logistic-Modified Weibull distribution is introduced as a new lifetime distribution based on the T-X family. Some properties of the new distribution are studied. Also, the estimation of the parameters is discussed using different methods such as maximum likelihood and Bayesian. The asymptotic variance-covariance matrix is obtained. Finally, we provide an application to real data.

No abstract

The Pareto distribution is a power law probability distribution that is used to describe social scientific, geophysical, actuarial, and many other types of observable phenomena. A new weighted Pareto distribution is proposed using a logarithmic weight function. Several statistical properties of the weighted Pareto distribution are studied and derived including cumulative distribution function, location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life, moments, shape indices such as skewness and kurtosis coefficients and order statistics. A parametric estimation is performed to obtain estimators for the distribution parameters using three different estimation methods the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution. The distribution is fitted to a real data set to show its importance in real life applications.