ISO* property of two-parameter compound Poisson distributions with applications

The ISO* property of noncentrality parameters is derived for the expected value of an ISO* function of independent nonnegative two-parameter compound Poisson random variables and is then applied to unbiasedness of tests and monotonicity of power functions of teals in an order-restricted hypothesis testing problem for the noncentrality parameter. The ISO* property and the Schur convexity are also studied for a class of two-parameter distributions which has the additive property (i.e., is closed under convolution) and contains the one-parameter family with the semigroup property as a special case. (C) 2000 Academic Press.