Characterization of the Pearson system of distributions based on reliability measures

LetX be a random variable andX ^(w) be a weighted random variable corresponding toX. In this paper, we intend to characterize the Pearson system of distributions by a relationship between reliability measures ofX andX ^(w), for some weight functionw>0.     

Measures of lack of fit from tests of chi-squared type

If X² is the Pearson chi-squared statistic for testing fit, then $\text{X}{}^2\text{n}$ has long been considered an associated measure of the degree of lack of fit. Here we consider two classes of statistics of chi-squared type, each having X² as a member. The first is a class of directed divergence statistics discussed by Cressie and Read, the second consists of nonnegative definite quadratic forms in the standardized cell frequencies. We investigate the large sample behavior of $\text{T}\text{n}$, where T is any of these statistics. A number of auxiliary results on the Cressie-Read statistics are also obtained. The measures are illustrated by application to data from classical physics compiled by Stigler.     

Chi-Squared Goodness-of-Fit Tests: Cell Selection and Power

To use the Pearson chi-squared statistic to test the fit of a continuous distribution, it is necessary to partition the support of the distribution into k cells. A common practice is to partition the support into cells with equal probabilities. In that case, the power of the chi-squared test may vary substantially with the value of k. The effects of different values of k are investigated with a Monte Carlo power study of goodness-of-fit tests for distributions where location and scale parameters are estimated from the observed data. Allowing for the best choices of k, the Pearson and log-likelihood ratio chi-squared tests are shown to have similar maximum power for wide ranges of alternatives, but this can be substantially less than the power of other well-known goodness-of-fit tests.     

Influence diagnostics in the Gamma regression model with adjusted deviance residuals

In this study, we develop the adjusted deviance residuals for the gamma regression model (GRM) by following Cordeiro's (2004) method. These adjusted deviance residuals under the GRM are used for influence diagnostics. A comparative analysis has been sorted out between our proposed method of the adjusted deviance residuals and an existing method for influence diagnostics. These results are illustrated by a simulation study and using a real data set. They are presented for different values of dispersion and sample sizes and indicate the significant role of the GRM inferences.     

Stringency-based ranking of normality tests

Many parametric statistical inferential procedures in finite samples depend crucially on the underlying normal distribution assumption. Dozens of normality tests are available in the literature to test the hypothesis of normality. Availability of such a large number of normality tests has generated a large number of simulation studies to find a best test but no one arrived at a definite answer as all depends critically on the alternative distributions which cannot be specified. A new framework, based on stringency concept, is devised to evaluate the performance of the existing normality tests. Mixture of t-distributions is used to generate the alternative space. The LR-tests, based on Neyman–Pearson Lemma, have been computed to construct a power envelope for calculating the stringencies of the selected normality tests. While evaluating the stringencies, Anderson–Darling (AD) statistic turns out to be the best normality test.     

Fourth moment results for mrbp and related power performance

A permutation test for analysing randomized block data was proposed by Mielke and Iyer (1982). They obtained the first three exact moments of this test statistic and approximated its permutation distribution by the Pearson type III distribution. Tracy and Khan (1991) derived the fourth exact moment of this test statistic to obtain a better approximating distribution. Here we obtain the simplified form of the fourth moment result for some special cases of this test statistic. Empirical powers for four treatments are compared, using this additional information, with those based on the three moment results, after simulating data from some underlying populations.     

The cornish-fisher expansion for estimating percentage points: a numerical perspective

The expansion, in standard form, consists of some 66 terms involving polyno - mials in a normal deviate, and cumulants and cumulant products to order ten. An assumed order of magnitude reduces these terms to eight groups. Sign patterns in the terms are not obvious. We take a number of Pearson densities and assess from the expansions a set of standard percentiles (1%, 5%, 95%, 99%). Validity of the as-sessments is pivoted on two alternative models:(i) the Bowman-Shenton algorithm for percentage points of Pearson densities, (ii) the 4-moment Johnson translation model. This approach has wide application since the models have proved to be remarkably reliable when compared, and also when compared with simulation as-sessments. A brief account is given of acceleration of convergence for the series, but there seems to be no analogue of the Padè or Levin algorithms.

The Cornish-Fisher application to the Fisher z-statistic is studied and the cumu- lants defined in general. Irwin's expression for the density of means from Pearson Type II is recalled. There is an error in the Cornish-Fisher treatment of the z-statistic but this is one which has its source in the write-up. Again the Irwin density in the general case has a factor missing.     

Identification of multiple influential observations in logistic regression

The identification of influential observations in logistic regression has drawn a great deal of attention in recent years. Most of the available techniques like Cook's distance and difference of fits (DFFITS) are based on single-case deletion. But there is evidence that these techniques suffer from masking and swamping problems and consequently fail to detect multiple influential observations. In this paper, we have developed a new measure for the identification of multiple influential observations in logistic regression based on a generalized version of DFFITS. The advantage of the proposed method is then investigated through several well-referred data sets and a simulation study.     

Modeling multiple‐response categorical data from complex surveys

Although “choose all that apply” questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to “choose all that apply” questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Variables that influence stakeholder satisfaction with the creation of corporate images of Thailand’s National Housing Authority

ABSTRACT

The project output will assist with the strategic planning and determination of communication tactics, coupled with public relations, to establish a good corporate image under fluctuating global circumstances. Questionnaires and non-experimental, in-depth interviews were used for both quantitative and qualitative research, respectively. The main objective of this study is to explore stakeholder attitudes and satisfaction with the creation of corporate images by Thailand’s National Housing Authority (NHA). The investigation of NHA stakeholders’ attitudes and comments toward the building of this government entity’s corporate image strategy led to sustainable developments within the NHA by determining concepts and research methods, crafting a research plan, and identifying the characteristics of the target group. This study includes other sections related to measuring the attitude index, data collection and analysis, comparisons and interpretations of the target group and stakeholder perspectives. The target population is comprised of: Residents in 68 communities under the governance of NHA and Thai citizens, executive directors of the Ministry of Social Development and Human Security (MSDHS), board committee, executive directors, and general staff, companies, the private sector, entrepreneurs, and building contractors, public relations staff. Overall, 30 categories of stakeholders were interviewed. Secondary information, such as project documents, was collected and utilized for action planning, which reflects stakeholder opinions towards the NHA. The survey sample size of stakeholders was limited to 400 people from 12 districts, comprising 31,844 households under the 68 NHA projects in Bangkok.