On the computation of noncentral chi-squared distributions

A computational formula for computing the cumulative distribution function of noncentral chi-squared distributions with odd degrees of freedom is given.     

A monte carlo study of some multivariate nonparametric statistics for profile analysis of several samples †

This paper describes the results of simulation studies on a class of nonparametric tests,T ₀, developed for the hypothesis of homogeneityH ₀, of several multivariate populations, and also on the class of testsT ₁, developed subsequently for the hypothesisH ₁, of parallelism of population profiles. Simulation studies relate to, first, the investigation of accuracy of the large-sample null-approximation for finite samples and, secondly, the study of powers under various types of alternatives to H ₀ and H ₁.     

Perturbation by multiplicative noise and the Simulation Extrapolation method

While most of the literature on measurement error focuses on additive measurement error, we consider in this paper the multiplicative case. We apply the Simulation Extrapolation method (SIMEX)—a procedure which was originally proposed by Cook and Stefanski (J. Am. Stat. Assoc. 89:1314–1328, 1994) in order to correct the bias due to additive measurement error—to the case where data are perturbed by multiplicative noise and present several approaches to account for multiplicative noise in the SIMEX procedure. Furthermore, we analyze how well these approaches reduce the bias caused by multiplicative perturbation. Using a binary probit model, we produce Monte Carlo evidence on how the reduction of data quality can be minimized. For helpful comments, we would like to thank Helmut Küchenhoff, Winfried Pohlmeier, and Gerd Ronning. Sandra Nolte gratefully acknowledges financial support by the DFG. Elena Biewen and Martin Rosemann gratefully acknowledge the financial support by the Federal Ministry of Education and Research (BMBF). The usual disclaimer applies.     

On simulating truncated skewed Cauchy random variables

Shirvani and Soltani suggested a method for characterizing and simulating one-sided truncated Cauchy random variables. For simulation, that involves solving a nonlinear transformation in each iteration. Here, we propose an alternative method to generate Cauchy random variables. Our method is more general (e.g., incorporates one-sided and two-sided truncations) and does not involve solving any equation. It can be implemented even using a hand calculator.     

Statistical inference for the availability of repairable system with general repair,reboot delay,and switching railure

We studied the inferences of an availability system with reboot delay and standby switching failures in which the system consisted of two operating units and one warm standby. The system was studied under the assumption that the time-to-failure and the time-to-repair were assumed to follow an exponential and a general distribution. The reboot times are assumed to be exponentially distributed with parameter β. We constructed a consistent and asymptotically normal estimator of availability for such a repairable system. Based on this estimator, interval estimation and testing hypothesis were developed by using logit transformation. To implement the simulation inference for the system availability, we adopted two repair-time distributions—namely, lognormal and Weibull; and three types of Weibull distributions—characterized by their shape parameters—were considered. Finally, appropriate tables and figures of all simulation results have been included.     

On accurate and precise generation of generalized Poisson variates

This article is concerned with comparison of a few random variate generation techniques for the generalized Poisson distribution. An evaluation is conducted on the degree of proximity between the estimates for its two distributional parameters and first four moments, and the specified or computed true population values via commonly accepted accuracy and precision measures in a simulated setting.     

A new confidence region for the multinomial distribution

A simple confidence region is proposed for the multinomial parameter. It is designed for situations having zero cell counts. Simulation studies as well as a real data application show that it performs at least as well as than at least two of the most common confidence regions.     

A parametric bootstrap approach for two-way error component regression models

In this article, the two-way error component regression model is considered. For the nonhomogenous linear hypothesis testing of regression coefficients, a parametric bootstrap (PB) approach is proposed. Simulation results indicate that the PB test, regardless of the sample sizes, maintains the Type I error rates very well and outperforms the existing generalized variable test, which may far exceed the intended significance level when the sample sizes are small or moderate. Real data examples illustrate the proposed approach work quite satisfactorily.     

Analysis of seasonal level shift (SLS) detection in SARIMA models

This study aims at exploring correct identification of seasonal outliers using most commonly applied test statistics. We evaluate the performance of seasonal level shift (SLS) by means of empirical level of significance, power of the test for sensitivity in detecting changes, and the vulnerability to masking of outliers by misspecification frequencies. We observe that the size of SLS affects the sampling distribution of η_SLS (test statistics for SLS detection) in case of SAR (1) and SMA (1) model. The empirical critical values for 1%, 5%, and 10% upper percentiles are higher than the usual cut off points and the empirical level of significance is inversely related to sample size and the model coefficients. The empirical power of the test statistics is not satisfactory at small sample size, and for large model coefficient. η_SLS gets confused with IO. The potential list of types of outliers should retain both IO and SLS as a part of outlier detection procedure for most efficient results. We apply the method suggested by Kaiser and Maravall with five possible types of outliers, that is, AO, IO, LS, TC, and SLS, to a number of quarterly and monthly time series data from Pakistan.     

Using plausible values in secondary analysis in large-scale assessments

Plausible values are typically used in large-scale assessment studies, in particular, in the Trends in International Mathematics and Science Study and the Programme for International Student Assessment. Despite its large spread, there are still some questions regarding the use of plausible values and how such use affects statistical analyses. The aim of this paper is to demonstrate the role of plausible values in large-scale assessment surveys when multilevel modeling is used. Different user strategies concerning plausible values for multilevel models as well as means and variances are examined. The results show that some commonly used user strategies give incorrect results while others give reasonable estimates but incorrect standard errors. These findings are important for anyone wishing to make secondary analyses of large-scale assessment data, especially those interested in using multilevel models to analyze the data.