عابدین حیدری

Consider two parallel systems with their component lifetimes following a generalized exponential distribution. In this paper, we introduce a region based on existing shape and scale parameters included in the distribution of one of the systems. If another parallel system's vector of scale parameters lies in that region, then the likelihood ratio ordering between the two systems holds. An extension of this result to the case when the lifetimes of components follow exponentiated Weibull distribution is also presented.

‎This paper examines the problem of stochastic‎ ‎comparisons of series and parallel systems with independent and heterogeneous components generalized linear failure rate‎. ‎First‎, ‎we consider two series system with possibly different parameters and obtain the usual stochastic order between the series systems‎. ‎Next‎, ‎we drive the usual stochastic order between parallel systems‎. ‎We also discuss the usual stochastic order between parallel systems by using the unordered majorization and the weighted majorization order between the parameters on the Ɗп.

In this paper، series and parallel systems، when the lifetimes of their components following the scale model are studied and different stochastic orderings between them are discussed. Moreover، we apply these results to the series and parallel systems consisting of exponentiated Weibull or generalized gamma components. The presented results in this paper complete and extend some known results in the literature.

Suppose there are two groups of random variables، one with independent and non-identical distributed and another with independent and identical distributed. In this paper، for the case when the size of groups are not equal، and all of the underlying random variables have exponential distribution، the necessary and sufficient conditions are obtained for establishing the mean residual life، hazard rate and dispersive orders between the second order statistics of two groups. Moreover، when random variables follow the Weibull distribution، the hazard rate، dispersive and likelihood ratio order between the second order statistics from two groups are investigated.

Suppose there are two groups of independent exponential random variables، where the first group has different hazard rates and the second group has common hazard rate. In this paper، the various stochastic orderings between their sample spacings have studied and introduced some necessary and sufficient conditions to equivalence of these stochastic ordering. Also، for the special case of sample size two، it is shown that the hazard rate function of the second sample spacing is Shcur-concave in the inverse vector of parameters.

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this issue in other distributions; in other words; whether or not the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. This paper aims to answer this question by presenting some concepts and introduce another family in which uncorrelation is equivalent to independence.