Tests for exponentiality against theM andLM-Classes of life distributions

This paper studies tests for exponentiality against the nonparametric classesM andLM of life distributions introduced by Klar and Müller (2003). The test statistics are integrals of the difference between the empirical moment generating function of given data and the moment generating function of a fitted exponential distribution. We derive the limit distributions of the test statistics in case of a general underlying distribution and the local approximate Bahadur efficiency of the procedures against several parametric families of alternatives to exponentiality. The finite sample behavior of the tests is examined by means of a simulation study. Finally, the tests under discussion are applied to two data sets, and we discuss the applicability of the tests under random censorship.     

Statistical discrimination of climate modification by urbanization

The statistical significance of observed changes in precipitation characteristics brought about by urbanization is investigated by using several statistical tests, including bivariatex ²,T ², likelihood ratio and conditional-t tests. Annual precipitation data from a number of stations in the LaPorte, St. Louis, Tulsa and Kansas City areas are analysed and the results are presented. The nature and limitations of these tests are discussed from the view points of assumptions made in the tests and the number of observations needed.     

Distribution models for nonparametric tests for fit in verifying complicated hypotheses and maximum-likelihood estimators. Part 1

Complicated-hypothesis testing is considered when the scalar or vector parameters of the probability distribution are calculated for a single sample. In that case, various factors influence the distributions of the statistics for the nonparametric tests for fit of Kolmogorov, Cramer–Mises–Smirnov, and Anderson–Darling. Revised results are given (tables of the percentage points and distribution models) for nonparametric tests of fit for verifying complicated hypotheses concerning a series of distributions when one uses maximum-likelihood estimators.     

Models for statistical distributions in nonparametric fitting tests on composite hypotheses based on maximum-likelihood estimators. Part II

Revised results are given as tables of the percentage points and distribution models for nonparametric fitting tests involved in checking composite hypotheses in terms of families of gamma distribution and a two-sided exponential distribution when one uses maximum likelihood estimators.     

Mathematical Theory of Probability and Statistics

Two test statistics are suggested for discriminating between the exponential model and the more general Weibull or gamma models, and these are compared to some previously used test statistics by Monte Carlo methods. The results of estimating reliability under an exponential assumption when the true model is Weibull is also investigated. These results as well as the tests mentioned above indicate that the exponential model is often not adequate when the more general models hold. In contrast to this result it was found that the Weibull model was quite robust relative to the generalized gamma distribution with regard to reliability estimation. Some general pivotal function properties are presented for the maximum likelihood estimator of reliability for the generalized gamma distribution and similar results also hold for the Weibull procedure under a generalized gamma assumption. These results made a Monte Carlo study of this problem feasible. Since the maximum likelihood estimators are apparently ill-behaved for smaller sample sizes and since the Weibull model is robust it appears little is gained by using the generalized gamma distribution for samples of size less than 200 to 400.     

Life Testing in Variably Scaled Environments

Typically, accelerated life-testing models postulate a specific functional relationship between the stress level at which an experiment is performed and the parameters of the assumed family of lifetime distributions. These models, and the statistical analyses that accompany them, are often criticized on the basis of the dubious validity of the assumed functional relationship and of the uncertainty involved in the extrapolation of experimental results to low stress levels at which little or no data have been obtained. This study focuses on an exponential factorial model for accelerated life tests that postulates that the lifetime distributions of different component types tested under varying environmental conditions are linked via environmental or component-related scale changes. Necessary and sufficient conditions are given for the identifiability of model parameters. For both censored and complete data, the derivation and properties of maximum likelihood estimates of these parameters are discussed in detail. Under the conditions that guarantee identifiability, the existence and the uniqueness of the maximum likelihood estimators are demonstrated, and their computation and large-sample behavior are discussed. In the final section, the model is fitted to published data from an accelerated life-testing experiment.     

-混合样本下缺失数据情形线性模型回归系数的经验似然比统计量的渐近分布

-混合的概念作为弱相关的衡量尺度在实际中被广泛应用,且缺失数据现象在各领域常有发生,已有文献对相依和缺失数据两种情形的统计推断分别进行了深入研究,但对同时存在相依和缺失数据情形的研究较少.本文研究既有相依又有缺失情形的统计推断,即研究-混合样本下缺失数据情形线性模型回归系数的经验似然比统计量的渐近分布.我们采取回归填补方法对响应变量的缺失值进行补足,得到线性模型回归系数的"完全"样本数据.在此基础上利用记分函数构造线性模型回归系数的经验似然比统计量,在一定条件下证明经验似然比统计量渐近服从卡方分布,这一结论为构造-混合样本下缺失数据情形线性模型回归系数的置信域提供了理论依据.     

Homogeneity and scale testing of generalized gamma distribution

The aim of this paper is to derive the exact distributions of the likelihood ratio tests of homogeneity and scale hypothesis when the observations are generalized gamma distributed. The special cases of exponential, Rayleigh, Weibull or gamma distributed observations are discussed exclusively. The photoemulsion experiment analysis and scale test with missing time-to-failure observations are present to illustrate the applications of methods discussed.     

Goodness-of-fit tests in mixed models

Mixed models, with both random and fixed effects, are most often estimated on the assumption that the random effects are normally distributed. In this paper we propose several formal tests of the hypothesis that the random effects and/or errors are normally distributed. Most of the proposed methods can be extended to generalized linear models where tests for non-normal distributions are of interest. Our tests are nonparametric in the sense that they are designed to detect virtually any alternative to normality. In case of rejection of the null hypothesis, the nonparametric estimation method that is used to construct a test provides an estimator of the alternative distribution.     

A semiparametric profile monitoring via residuals

Profile monitoring is a vast area of research underneath the statistical process monitoring (SPM). Several methods for univariate and multivariate process control are found in literature to monitor the profile data, including parametric, nonparametric, and some semiparametric methods. The main idea behind monitoring the linear profiles in mixed effects is to model the possible individual differences between similar set of profiles for future monitoring. In this paper, nonparametric and semiparametric approaches are proposed to model the profile data in a linear mixed effect setting by considering the residuals from a parametric model. A simulation study was carried out to compare the efficiency of the proposed methods. At first step, the residuals from a parametric linear mixed model are obtained. A nonparametric approach (NPR) is then used to model these residuals. Finally, a semiparametric method (MMRRPM) is proposed as a convex combination of the parametric (P) and nonparametric estimations based on the residuals (NPR) to model the profile data in mix effects. Two Hoteling's T² statistics were computed for each technique based on fitted values and the estimated random effects. The results show that the proposed methods are most effective to monitor the autocorrelated profile data compared with the state‐of‐the‐art.