Cramér-von Mises tests of fit for the Poisson distribution

Goodness-of-fit tests based on the Cramér-von Mises statistics are given for the Poisson distribution. Power comparisons show that these statistics, particularly A², give good overall tests of fit. The statistic A² will be particularly useful for detecting distributions where the variance is close to the mean, but which are not Poisson.     

A moment test to identify uniformity

An omnibus test of uniformity based upon the ratios of sample moments and population moments is introduced. Results of a monte carlo power study show that for two types of alternatives considered, the proposed test has good power in comparison with Neyman's test N ₂Greenwood's test, Kolmogorov-Smirnov test, and Chi-squared test.     

New Goodness of Fit Tests Based on Stochastic EDF

A new approach of randomization is proposed to construct goodness of fit tests generally. Some new test statistics are derived, which are based on the stochastic empirical distribution function (EDF). Note that the stochastic EDF for a set of given sample observations is a randomized distribution function. By substituting the stochastic EDF for the classical EDF in the Kolmogorov–Smirnov, Cramér–von Mises, Anderson–Darling, Berk–Jones, and Einmahl–Mckeague statistics, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. In comparison to existing tests, it is shown, by a simulation study, that the new test statistics are generally more powerful than the corresponding ones based on the classical EDF or modified EDF in most cases.     

A New Exponential GOF Test for Data Subject to Multiply Type II Censoring

This article presents a new goodness-of-fit (GOF) test statistic for multiply Type II censored Exponential data. The new test also applies to ordinary Type II censored samples and complete samples, since those cases are special cases of multiply Type II censoring. This test statistic is based on a ratio of linear functions of order statistics. Empirical power studies confirm that this ratio test compares favorably to currently available GOF tests for ordinary Type II censored data. Three data analysis examples are provided that demonstrate the usefulness of this new test statistic.     

Testing Normality for Linear AR( p ) Models

Abstract

This paper proposes a nonparametric mixed test for normality of linear autoregressive time series. The test is based on the best one-step forecast in mean square with time reverse. The test statistic is the mixture of a goodness of fit statistic and Cramer–Von Mises statistic. Some asymptotic properties are developed for the test. Simulated results have shown that the test is easy to use and has good powers. Three examples of applying the test to real data are also included.     

Evaluation of Beta Generation Algorithms

In this article, we discuss the maximum likelihood estimates (MLEs) for the exponential and Weibull distributions by considering progressive Type-I interval censored data. For exponential distribution, the explicit expression of MLE of failure rate cannot be obtained when the intervals are not equal in length. The direct application of some numerical algorithms, such as the Newton–Raphson algorithm, is non-ideal because of the cumbersome second derivative. We apply some equivalent quantities to obtain the MLE of failure rate of exponential distribution. Based on the equivalent quantities and the Weibull-to-exponential transformation technique, we propose a new algorithm to obtain the MLEs for the parameters of progressive Type-I interval Weibull data. An example reanalysis and some simulation studies are carried out to illustrate the performance of the estimations using the new algorithm.     

Statistical Analysis for the Inverse Trinomial Distribution

This article considers parameter estimation, goodness of fit, likelihood ratio and score tests, and model selection by Akaike information criterion for the inverse trinomial (IT) distribution, a classical one-dimensional random walk distribution. The IT distribution has a cubic variance function of the mean and is a generalization of the negative binomial distribution. Basic distributional properties and expressions for the probability mass function, recurrence formula, moments, and score functions are also presented.