In this study, we have considered a series system composed of stochastically independent M-component where M is a random variable having the zero truncated modified discrete Lindley distribution. This distribution is newly introduced by transforming on original parameter. The properties of the distribution of the lifetime of above system have been examined under the given circumstances and also parameters of this new lifetime distribution are estimated by using moments, maximum likelihood and EM-algorithm.
In this study, at …rst a new polynomial rank transmutation is proposed. Then, a new cubic rank transmutation is introduced by simplifying the set of transmutation parameters in order to improve its usefulness in statistical modeling. The purpose of this comment is to clarify some issues that exist in the methodology of obtaining the distribution by the cubic transmutation and the stage of proo…ng it. In this way, both the parameter space is expanded and the process of establishing the cubic transformed distribution family is given.
Regarding the concept of quadratic rank transmutation, a new distribution with convex combinations of the life distributions of two-component systems (series and parallel systems) whose component lifetimes are not identical is obtained. This proposed distribution has extra parameters compared to the known transmuted distribution. It can also be represented by two different baseline distributions. So, it is very ‡exible in modeling. A description of the various structural properties of the subject distribution along with its reliability behavior is provided. Finally, a real data analysis is performed for this distribution and it is found that this class is more ‡exible.
A functional composition of the distribution function of one probability distribution with the inverse distribution function of another is called the transmutation map. The present paper is purported to show how the transmuted distribution can be obtained by using the convex combination of failure probability of two-component systems. The transmuted Gumbel univariate exponential distribution is presented by changing convex combination parameter. This new distribution is de…ned and studied. Some mathematical properties of this distribution including the generating function and ordinary moments are derived. The survival, hazard rate and mean residual life functions are discussed. Finally, three applications to real data are presented.
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