A new generalized family of distributions called the odd power generalized weibull-G family of distributions is developed. Some properties of the new family of distributions including quantile function, moments, incomplete and probability weighted moments, distribution of the order statistics and Ré, nyi entropy are derived. Estimation of model parameters using maximum likelihood estimation technique and simulation study to examine the bias and mean square error are discussed. Applications to real data sets to illustrate the applicability of the generalized family of distributions is also given.

We develop a generalized distribution, namely, exponentiated half logistic log-logistic weibull distribution. Several structural properties of the distribution including expansion of density, distribution of order statistics, Ré, nyi entropy, moments, probability weighted moments, quantile function, generating function, and maximum likelihood estimates were derived. A simulation study to examine the consistency of the maximum likelihood estimates was conducted. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed model.

In this paper we focus on two topics. Firstly, we propose $U$-statistics for the weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondly, due to lack of a comprehensive comparison between the weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. In our knowledge, this work is the most comprehensive comparison study for the estimators for the weibull distribution. Based on simulations, it turns out that different estimators may appeal for different range of the parameters. So, practitioners are allowed to chose the best estimator that is suggested by the goodness-of-fit criteria.

In this paper we introduce a new scheme of censoring and study it under the weibull distribution. This scheme is a mixture of progressive Type II censoring and self relocating design which was first introduced by Srivastava [8]. We show the superiority of this censoring scheme (PSRD) relative to the classical schemes with respect to “asymptotic variance”. Comparisons are also made with respect to the total expected time under experiment (TETUE) as an important feature of time and cost saving. These comparisons show that TETUE(SRD)<TETUE(PSRD)<TETUE(PC2) if 0<b<1, TETUE(PSRD)=TETUE(SRD)<TETUE(PC2) if b=1 and TETUE(PSRD) is the best among all the designs if b = 2 (Rayleigh distribution case).

A new family of distributions referred to as the exponentiated half logistic odd weibull-Topp-Leone-G family of distributions is developed. We derive statistical properties of the new family of distributions. The distribution can be expressed as a linear combination of the exponentiated-G distribution. Five special cases for the new family of distributions are also presented. Estimation and Monte Carlo simulation study was also conducted. Two real data examples for a selected special case are also presented.

This paper deals with the problem of reconstructing missing data in a left type-II censoring scheme, where the underlying distribution is the weibull distribution. Frequentist and Bayesian approaches are adopted in order to provide some point reconstructors for the past failure times. The problem of determining reconstruction intervals for the past failure times is also considered. The investigation includes an example of application to real data and various comparisons based on Monte Carlo simulations.