A regression-type method of estimating the four parameters of a stable distribution is presented. The estimators found are consistent and approximately unbiased for moderately large sample sizes. Their efficiencies, found through a simulation study, are greater than those of most other estimators for large portions of the parameter space. Moreover, the amount of computation involved is minimal and apparently less than that needed by the methods of Paulson, Holcomb, and Leitch (1975) and of maximum likelihood (DuMouchel 1971). Finally, this method is applied to stock price data from four corporations.

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Abstract. Although the Pearson type 3 (P3) is one of the basic models in statistical hydrology, its use to model untransformed data has been restrained because of difficulties encountered in fitting this distribution by traditional methods. In this paper an adaptive estimation procedure of mixed moments for the P3 family is introduced which is based on several fractional moments of the exponentially transformed data and the mean of the original data. The procedure is easy to implement in small samples and is valid over the entire parameter space. Explicit formulae for the variances and covariances of parameter estimators and of the variance of the T-year event are derived. In addition, two variants of the new procedure are compared with two versions of the method of moments and a version of the method of conditional moments via Monte Carlo simulation. With samples generated from P3 populations, it is found that one of the variants of the new procedure is the best overall method in estimating 100-year flood events, and the other variant is best in estimating the median and 10-year low-flow events. The good performance of these two variants is also observed in samples generated from alternatives to P3 distributions. A modification of the procedure is also introduced and investigated when a prior assumption of positive skewness is adopted.

Savage score statistics are employed to develop a test for comparing survival distributions with right-hand singly censored data. The procedure is motivated by the interest in developing a powerful method for determining differences when true survival distributions cross. Examination of small-sample characteristics under the null hypothesis indicate that asymptotic critical values yield a slightly conservative test. Power of the test compares favorably with other criteria, including the modified Smirnov procedure, particularly if there is a single crossing of the survival curves.