On the mixture of the inverse Gaussian distribution with its complementary reciprocal
通过推广逆高斯分布函数，得到一个新的三参数分布族，它包含逆高斯分布和倒数逆高斯分布作为特例，并保留了逆高斯分布的一些有趣性质。该分布可表示为逆高斯分布与其互补倒数分布的混合，适用于正偏态单峰数据，特别是持续时间或失效时间数据。
By generalizing the inverse Gaussian distribution function, we obtain a new three- parameter family of distributions which includes as special cases the inverse Gaussian and the reciprocal inverse Gaussian distributions, while preserving some of the interesting properties of the inverse Gaussian distribution. We derive two representations of the new distribution, one as the mixture of an inverse Gaussian distribution with its complementary reciprocal, and the second as a sum of an inverse Gaussian variable and an independent compound Bernoulli variable. The family is a two-parameter exponential model for known value of the third parameter, and is intimately related with exponential dispersion model theory. We also consider estimation and inference properties for the family, and show that it may have applications for positive right-skewed unimodal data and, in particular, duration or failure-time data.