Abstract If the distribution of the linear combination of two independent and identically distributed random variables from a distribution belongs to the same distribution, then we call that distribution a stable distribution. The Levy distribution is a member of the family of stable...

In this paper, we investigate a random contraction scheme proposed by Wesolowski and Ahsanullah (2004. Austral. NZ J. Statist. 46, 297-303). Random contraction is used in the record and order statistics settings. Some distributional recurrence relations were found for the probability density...

In this paper, we derive the distribution of life length of a parallel system with random number of components when the life distribution of each component follows a Weibull distribution and the number of components follows a Poisson distribution truncated at zero. For two independent such...

In life-testing and survival analysis, sometimes the components are arranged in series or parallel system and the number of components is initially unknown. Thus, the number of components, say <italic>Z</italic>, is considered as random with an appropriate probability mass function. In this paper, we model the...

Jorgensen <italic>et al</italic>. [14] introduced a three-parameter generalized inverse Gaussian distribution, which is a mixture of the inverse Gaussian distribution and length biased inverse Gaussian distribution. Also Birnbaum--Saunders distribution is a special case for <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cjas_a_567251_o_ilm0001.gif"/> </inline-formula>, where <italic>p</italic> is the mixing parameter....