We apply a recently developed computational approach‎ ‎test (CAT) to the one-way fixed effects ANOVA models of log-normal‎ ‎data with unequal variances‎. ‎The merits of the proposed test are‎ ‎numerically compared with the existing tests‎ - ‎the James second‎ ‎order test‎, ‎the Welch test and the Alexander-Govern test‎ - ‎with‎ ‎respect to their sizes and powers in different combinations of‎ ‎parameters and various sample sizes‎. ‎The simulation results‎ ‎demonstrate that the proposed method is‎ ‎satisfactory‎: ‎its type I error probability is very close to the nominal level‎. ‎We illustrate these approaches using a real example.

In this paper‎, ‎some recurrence relations are presented for the single and product moments of progressively Type-II right censored order statistics from a Pareto distribution‎. ‎These relations are obtained for a progressively censored sample from Pareto distribution with fixed and random removals‎, ‎where in the random case‎, ‎the number of units removed at each failure time follows a binomial distribution‎. ‎In addition‎, ‎Thomas-Wilson's Mixture Formula for Moments are obtained with with fixed and random removals‎. ‎Finally‎, ‎a numerical study is carried out to compare real and simulation results based on biases and MSEs of the expected termination time.

In this paper, a new method has been proposed to incorporate an extra parameter to a family of lifetime distributions for more flexibility. A special sub-case has been considered in details namely; two parameter Weibull distribution. Various mathematical properties of the proposed distribution, including explicit expressions for the moments, quantiles, moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. A simulation study is conducted to evaluate the performances of these estimators. For the illustrative purposes, two data sets have been analyzed to show how the proposed model work in practice.

This article deals with the problem of characterizing the parent distribution on the basis of the cumulative residual entropy of‎ ‎sequential order statistics under a conditional proportional hazard rates model‎. ‎It is shown that the equality of‎ ‎the cumulative residual entropy in the first sequential order statistics determines uniquely the parent distribution‎. ‎Subsequently‎, ‎we characterize the Weibull distribution on the basis of the ratio of the‎ ‎cumulative residual entropy of first sequential order statistics to the corresponding mean‎. ‎Also‎, ‎we consider characterizations based on‎ ‎the dynamic cumulative residual entropy and derive some bounds for the cumulative residual‎ ‎entropy of residual lifetime of the sequential order statistics.

In this paper‎, ‎a new method has been proposed to introduce an extra parameter to a family of lifetime distributions for more flexibility‎. ‎A special sub-case has been considered in details namely; two parameters Weibull distribution‎. ‎Various mathematical properties of the proposed distribution‎, ‎including explicit expressions for the moments‎, ‎quantile‎, ‎moment generating function‎, ‎residual life‎, ‎mean residual life and order statistics are derived‎. ‎The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms‎, ‎and they have to be obtained by solving non-linear equations only‎. ‎A simulation study is conducted to evaluate the performances of these estimators‎. ‎For the illustrative purposes‎, ‎two data sets have been analyzed to show how the proposed model work in practice.

Based on the generalized log-logistic family (\cite {Gleaton:Lynch:2006}) of distributions‎, ‎we propose a new family of continuous distributions‎ ‎with two extra shape parameters called the exponentiated odd log-logistic family‎. ‎It extends the class of exponentiated distributions‎, ‎odd log-logistic family (\cite {Gleaton:Lynch:2006}) and any continuous distribution by adding two shape parameters‎. ‎Some special cases of this family are discussed‎. ‎We investigate the shapes of the density and hazard rate functions‎. ‎The proposed family has also tractable properties such as various explicit expressions for the ordinary and incomplete moments‎, ‎quantile and generating functions‎, ‎probability weighted moments‎, ‎Bonferroni and Lorenz curves‎, ‎Shannon and R\'{e}nyi entropies‎, ‎extreme values and order statistics‎, ‎which hold for any baseline model‎. ‎The model parameters are estimated by maximum likelihood and the usefulness of the new family is illustrated by means of three real data sets.