Modified proportional hazard rates and proportional reversed hazard rates models via Marshall–Olkin distribution and some stochastic comparisons

Adding parameters to a known distribution is a useful way of constructing flexible families of distributions. Marshall and Olkin (1997) introduced a general method of adding a shape parameter to a family of distributions. In this paper, based on the Marshall–Olkin extension of a specified distribution, we introduce two new models, referred to as modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models, which include as special cases the well-known proportional hazard rates and proportional reversed hazard rates models, respectively. Next, when two sets of random variables follow either the MPHR or the MPRHR model, we establish some stochastic comparisons between the corresponding order statistics based on majorization theory. The results established here extend some well-known results in the literature.     

对"媒介即讯息"的再审视

"媒介即讯息"是加拿大传播学者麦克卢汉于20世纪60年代提出的著名论断,它曾被誉为媒介研究的"哥白尼革命",即扭转了以往媒介研究偏重于媒介内容的局面,将注意力引向传播媒介本身。在报纸、广播、电视占据主导位置的大众传播时代,"媒介即讯息"理论并未受到应有的重视,甚至被贬斥为"技术决定论"。而在互联网兴起之后,媒介技术的发展及其对人和社会构型的影响越来越显著,"媒介即讯息"作为媒介研究技术取向的开创性理论,在媒介技术飞速发展的时代背景下对其进行内涵外延的廓清,具有重要的现实意义。     

On the Harris extended family of distributions

A new method for generating new classes of distributions based on the probability-generating function is presented in Aly and Benkherouf [A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70–80]. In particular, they focused their interest to the so-called Harris extended family of distributions. In this paper, we provide several general results regarding the Harris extended models such as the general behaviour of the failure rate function. We also derive a very useful representation for the Harris extended density function as an absolutely convergent power series of the survival function of the baseline distribution. Additionally, some stochastic order relations are established and limiting distributions of sample extremes are also considered for this model. These general results are illustrated in several special Harris extended models. Finally, we discuss estimation of the model parameters by the method of maximum likelihood and provide an application to real data for illustrative purposes.