A modification of the Fisher-Cornish approximation for the student t percentiles

An asymptotic expansion of the Student t distribution is derived by expanding the standardized Student t distribution in terms of the normal distribution. This expansion is inverted to obtain corresponding asymptotic expansions for the Student t percentiles as functions of the standard normal percentiles0 Using the first two, three or four terms of these expansions, we get approximations of the Student t percentiles which are generally more accurate than the approximations given by Fisher and Cornish(1960) and Koehler (1983).An approximation of the distribution function obtained from this expansion is compared with the approximations discussed by Ling (1978) andfound to be more accurate for moderate degrees of freedom.     

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.     

Sufficient Conditions for the Existence of a Solution for the Log-Likelihood Equations in the Three-Parameter Gamma Distribution

The existence of maximum likelihood estimators for the three-parameter gamma distribution is still an open problem. It demands the solution of the system of the log-likelihood equations which can be solved only with the use of numerical methods. The aim of this article is to provide sufficient conditions for the existence of a solution for the system of the log-likelihood equations. The conditions are expressed in terms of the geometric, arithmetic, and harmonic mean. Also, the importance of the sign of the third central moment for the existence of a solution is revealed.     

Analysis of Linear Models with Two Factors Having Both Fixed and Random Levels

A general theory for a case where some factors have both fixed and random effect levels is developed under a two-way treatment structure model. This is an extension of a one factor with both fixed and random levels (Njuho and Milliken, 2005 Njuho , P. M. , Milliken , G. A. ( 2005 ). Analysis of linear models with one factor having both fixed and random levels . Commun. Statist. Theor. Meth. 34 : 1979 – 1989 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We consider several alternative approaches for estimating the fixed effects and the variance components using mixed models. We propose conducting the analysis in stages depending on the hypothesis being tested. The computational procedures are illustrated using two numerical examples.     

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.     

A Proportional Odds Beta-Binomial Model for Evaluating the Effect of Treatment in Cross-Over Studies with Baseline Covariates: An Application to Condom Failure Data

Cross-over trials with correlated Bernoulli outcomes are common designs. In condom functionality studies, for example, an indicator of condom failure is reported for each sex act using standard or experimental condoms. Two popular analysis methods for such data are Generalized Estimating Equations and logit-normal random effects models. An alternative random effects model, the beta-binomial, is commonly used in contexts involving only between-cluster effects. The flexibility of the beta distribution and the interpretation of random effects as cluster-specific failure probabilities make it appealing, and we consider an extension of the model to account for within-cluster treatment effects using proportional odds assumptions.     

E‐Business: A Review of Research Published in Production and Operations Management (1992–2008)

We review, classify, consolidate, and synthesize the contributions to the expanding field of e‐business that have been published in Production and Operations Management. We classify e‐business research in the following four categories: (1) e‐auctions, (2) radio frequency identification, (3) e‐business system design, and (4) competition, conflict, collaboration, and coordination (C⁴ in e‐business). We identify important research themes, research methodologies, and research techniques within each of these categories. We also provide directions for future research and discuss the managerial implications of the e‐business research reported in our paper.     

The Lehmann Model with Time-dependent Covariates

Consider the Lehmann model with time-dependent covariates, which is different from Cox’s model. We find out that (1) the parameter space for β under the Lehmann model is restricted, and the maximum point of the parametric likelihood for β may lie outside the parameter space; (2) for some particular time-dependent covariate, under the standard generalized likelihood the semiparametric maximum likelihood estimator (SMLE) is inconsistent and we propose a modified generalized likelihood which leads to the consistent SMLE.