George C. Canavos

Estimation in the Pearson type 3 distribution

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.

Estimation in the three-parameter inverse Gaussian distribution

A mixed moments method for the estimation of parameters in the three-parameter inverse Gaussian distribution (IG3) is introduced. The method is an adaptive iterative procedure, which combines the method of moments with a regression method based on the empirical moment generating function. Monte Carlo results indicate that the new procedure is more efficient than alternative estimation methods (including the maximum likelihood) over large portions of the parameter space with samples of small or moderate size. Asymptotic results are also obtained and may be used to draw approximate inferences with small samples. Two data sets are used to illustrate estimation and testing procedures and to construct exploratory graphs for the appropriateness of the IG3 model.

Estimation in the three-parameter gamma distribution based on the empirical moment generation function

The empirical moment generating function is used for the estimation of the shape, scale, and location parameters of a three-parameter gamma distribution. The proposed method is valid over the entire parameter space and avoids the difficulties associated with maximum likelihood estimation when the sample has a very large positive skewness. In addition, finite sample results from a simulation study indicate that the new procedure is more accurate than recently proposed modifications of both moment and maximum likelihood methods over important portions of the parameters space.

The Robustness of Two-Sided Tolerance Limits for Normal Distributions

The robustness of two-sided tolerance limits for normal distributions is examined based on a computer simulation in which the Students t and gamma distributions are used as generating models. Results indicate that the normal tolerance limits are sensit..

Testing the Fit of Gamma Distributions Using the Empirical Moment Generating Function

ABSTRACT This article presents goodness-of-fit tests for two and three-parameter gamma distributions that are based on minimum quadratic forms of standardized logarithmic differences of values of the moment generating function and its empirical counterpart. The test statistics can be computed without reliance to special functions and have asymptotic chi-squared distributions. Monte Carlo simulations are used to compare the proposed test for the two-parameter gamma distribution with goodness-of-fit tests employing empirical distribution function or spacing statistics. Two data sets are used to illustrate the various tests.

A merit pay allocation model for college faculty based on performance quality and quantity

Abstract The salary of most college and university faculty in the United States is based on merit and market factors, rather than on a fixed scale. This article proposes a structured model for faculty performance evaluation that explicitly considers both quality and quantity of faculty output in the areas of teaching, scholarship, and service. Detailed criteria for measuring the quantity of performance outputs and for assigning quality weights are presented. The model allows faculty to emphasize different aspects of their work, e.g. teaching or scholarship. The model proposes merit pay allocation in proportion to a faculty members contribution to a departments overall performance output.

Cumulant Plots for Assessing the Gamma Distribution

This article introduces graphical procedures for assessing the fit of the gamma distribution. The procedures are based on a standardized version of the cumulant generating function. Plots with bands of 95% simultaneous confidence level are developed by utilizing asymptotic and finite-sample results. The plots have linear scales and do not rely on the use of tables or values of special functions. Further, it is found through simulation, that the goodness-of-fit test implied by these plots compares favorably with respect to power to other known tests for the gamma distribution in samples drawn from lognormal and inverse Gaussian distributions.

The sensitivity of the one-sample and two-sample student t statistic

By Monte Carlo simulation, this study illustrates and summarizes the extent of robustness of the one-sample and two-sample Student t statistics for inferences on means to the assumptions of normality and/or equal variances when very small sample sizes are involved. It is determined that in a relative sense the two-sample t statistic is more robust to the assumption of normality than the one-sample statistic, if equal sample sizes are used. Whereas the robustness of the two-sample statistic is truly exceptional for both the normality and equal variance assumptions when n1 = n2, that of the one-sample statistic appears to be restricted to situations in which the underlined distribution is either symmetrical or only modestly skewed. The robustness of the two-sample statistic deteriorates considerably when the sample sizes differ by a factor of two or more. Therefore, the best protection available to a practitioner for the one-sample case is to use relatively large sample sizes, say around 25 to 30 observations, and to use equal sample sizes for the two-sample case.

Sensitivity of a Bayesian inference to prior assumptions

The sensitivity of-a Bayesian inference to prior assumptions is examined by Monte Carlo simulation for the beta-binomial conjugate family of distributions. Results for the effect on a Bayesian probability interval of the binomial parameter indicate that the Bayesian inference is for the most part quite sensitive to misspecification of the prior distribution. The magnitude of the sensitivity depends primarily on the difference of assigned means and variances from the respective means and variances of the actually-sampled prior distributions. The effect of a disparity in form between the assigned prior and actually-sampled distributions was less important for the cases tested.

An analysis of the variation in billing charges of medical providers: causes and implications

The purpose of this paper is to review the billing methodology of physicians that participate in fee-for-service plans, and, using a data set of billing charges, determine the significance of the variation in fees by providers of certain kind of procedures. Providers use cost-plus pricing and take into account the medical aspects of the services and market forces. Using the Current Procedural Terminologies (CPT) established by the American Medical Association, the providers define the medical services by the six digit CPT code, and bill accordingly. The statistical evidence shows that there is some evidence that fees of providers who bill under the ‘medicine’ codes tend to exhibit more variation in charges than other procedures.