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....