A Family of Random Variables Closed under Reciprocation

Some of the known properties of a particular family of distributions derived as a model for fatigue failure by Birnbaum and Saunders [3] are shown to hold for a class of families. These results stem from the fact that each variate in the class suitably scaled has the same distribution as its reciprocal. This clarifies the utility of certain distributions proposed for fatigue life, e.g., lognormal. This property also influences the estimation of the scale parameter and makes possible the solution of two important practical problems, a special solution of which had been presented in Saunders [11].