Least-squares estimation of distribution functions in johnson's translation system

Abstract

Abstract To summarize a set of data by a distribution function in Johnson's translation system, we use a least-squares approach to parameter estimation wherein we seek to minimize the distance between the vector of "uniformized" oeder statistics and the corresponding vector of expected values. We use the software package FITTRI to apply this technique to three problems arising respectively in medicine, applied statistics, and civil engineering. Compared to traditional methods of distribution fitting based on moment matching, percentile matchingL 1 estimation, and L ⌆ estimation, the least-squares technique is seen to yield fits of similar accuracy and to converge more rapidly and reliably to a set of acceptable parametre estimates. Keywords: Distribution fittingJohnson's translation system L 1 estimation L ⌆ estimationnonlinear weighted least-squares estimation