Weighted inverse Gaussian -- a versatile lifetime model

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. It is observed that the estimators of the unknown parameters can be obtained by solving a three-dimensional optimization process, which may not be a trivial issue. Most of the iterative algorithms are quite sensitive to the initial guesses. In this paper, we propose to use the EM algorithm to estimate the unknown parameters for complete and censored samples. In the proposed EM algorithm, at the M-step the optimization problem can be solved analytically, and the observed Fisher information matrix can be obtained. These can be used to construct asymptotic confidence intervals of the unknown parameters. Some simulation experiments are conducted to examine the performance of the proposed EM algorithm, and it is observed that the performances are quite satisfactory. The methodology proposed here is illustrated by three data sets.