Consider the problem of deriving method-of-moments estimates for the threeparameters
Chapter 10, Problem 2(choose chapter or problem)
Consider the problem of deriving method-of-moments estimates for the threeparameters , 1, and 2 of a two-stage hyperexponential distribution. Clearly,three sample moments will be needed for this purpose. But if we have only thesample mean x and the sample variance s2 available, we can solve the problemby imposing a restriction on the parameters. Assume that11 + 2=1+1 22is the chosen restriction. Show that the method-of-moments estimates of theparameters are given by (assuming that s2 x2)1, 2 = 1x 1xs2 x2s2 + x2 (10.1)and = 1(2x 1)2 1. (10.2)
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