Transformed beta Distribution and Its Application in Distribution Fitting

摘要

We consider the transformation Y = alpha + beta (X/sup gamma / - (1 - X) /sup delta/), - infinity < alpha , beta , gamma ,delta < infinity, on the beta variate X which has the p.d.f. f(x) = x/sup p-1/(1 - x)/sup q-1//B (p, q), 0 less than or equal to x less than or equal to 1, where B(p, q) is the beta function. This family includes a number of well-known distribution functions, one of them is the generalized Tukey's lambda distribution. Using this family of distributions as base, moment models are constructed for the theoretical distribution of sample statistics. Significance of these models is: Producing the correct range in the distribution of the statistics, consistent with the asymptotic normality of the statistics, and in some models higher order standard moments up to beta sub 4 are used. (ERA citation 07:062376)