Gini index based goodness-of-fit test for the logistic distribution

To model growth curves in survival analysis and biological studies the logistic distribution has been widely used. In this article, we propose a goodness-of-fit test for the logistic distribution based on an estimate of the Gini index. The exact distribution of the proposed test statistic and also its asymptotic distribution are presented. In order to compute the proposed test statistic, parameters of the logistic distribution are estimated by approximate maximum likelihood estimators (AMLEs), which are simple explicit estimators. Through Monte Carlo simulations, power comparisons of the proposed test with some known competing tests are carried. Finally, an illustrative example is presented and analyzed.     

Gender as a Moderator of the Relation Among Social Support Functions and Life Satisfaction in Older Malaysians

The aim of this study was to examine the moderating role of gender on relations among social support functions and life satisfaction in older Malaysians. The study sample was 1,800 older residents in a community; all were at least 60 years old. This study was a cross-sectional and corelational survey, and the data were collected by multistage stratified sampling. This study revealed that fewer social support functions, and therefore less life satisfaction, were available for females than for males. The results of moderated regression analyses demonstrated that gender interacted only on the relationship between positive social interaction support and tangible support with life satisfaction. Specifically, at a high tangible support level, females had lower life satisfaction when compared to a low tangible support level. There may be a need for new programs and services to provide other aspects of social support to older female adults to improve and maintain life satisfaction in later life.     

Moments of nonparametric probability density functions of entropy estimators applied to testing the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model data and then it is important to develop efficient goodness of fit tests for this distribution. In this article, we introduce some new test statistics for examining the IG goodness of fit based on correcting moments of nonparametric probability density functions of entropy estimators. These tests are consistent against all alternatives. Critical points and power of the tests are explored by simulation. We show that the proposed tests are more powerful than competitor tests. Finally, the proposed tests are illustrated by real data examples.     

Toward the evaluation of P(X(t) > Y(t)) when both X(t) and Y(t) are inactivity times of two systems

The inactivity time, also known as reversed residual life, has been a topic of increasing interest in the literature. In this investigation, based on the comparison of inactivity times of two devices, we introduce and study a new estimate of the probability of the inactivity time of one device exceeding that of another device. The problem studied in this paper is important for engineers and system designers. It would enable them to compare the inactivity times of the products and, hence to design better products. Several properties of this probability are established. Connections between the target probability and the reversed hazard rates of the two devices are established. In addition, some of the reliability properties of the new concept are investigated extending the well-known probability ordering. Finally, to illustrate the introduced concepts, many examples and applications in the context of reliability theory are included.     

New influence diagnostics in ridge regression

We occasionally find that a small subset of the data exerts a disproportionate influence on the fitted regression model. We would like to locate these influential points and assess their impact on the model. However, the existence of influential data is complicated by the presence of collinearity (see, e.g. [15 E. Walker and J. Birch, Influence measures in ridge regression, Technometrics 30 (1989), pp. 221–227. doi: 10.1080/00401706.1988.10488370[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]). In this article we develop a new influence statistic for one or a set of observations in linear regression dealing with collinearity. We show that this statistic has asymptotically normal distribution and is able to detect a subset of high ridge leverage outliers. Using this influence statistic we also show that when ridge regression is used to mitigate the effects of collinearity, the influence of some observations can be drastically modified. As an illustrative example, simulation studies and a real data set are analysed.     

Simple graphs and bounds for the elements of the hat matrix

In regression analysis, the matrix H = X (XTX)-1XT is known as the 'hat' or 'projection' matrix, among other names. It has been studied by many authors from different perspectives. The main area of study has been the type of measure best adapted to detect leverage points in linear regression. For computational reasons, these measures were originally based on the diagonal elements of the hat matrix. In the present paper, we propose a very simple procedure for identifying leverage groups. The procedure is based on upper and lower bounds for the diagonal and the off-diagonal elements of H. These upper and lower bounds can easily be shown on an index plot of the elements of H.     

Entropy-based tests of uniformity: A Monte Carlo power comparison

In this article, we consider different entropy estimators and propose some entropy-based tests of uniformity. Critical values of the proposed test statistics are obtained by Monte Carlo simulation. Then the power values of the tests for various alternatives and sample sizes are compared. Finally, some recommendations for the application of the proposed tests in practice are presented.     

On the estimation of extropy

Recently, Lad, Sanfilippo, and Agro [(2015), ‘Extropy: Complementary Dual of Entropy’, Statistical Science, 30, 40–58.] showed the measure of entropy has a complementary dual, which is termed extropy. The present article introduces some estimators of the extropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made with Qiu and Jia’s estimators [(2018a), ‘Extropy Estimators with Applications in Testing uniformity’, Journal of Nonparametric Statistics, 30, 182–196]. The results indicate that the proposed estimators have a smaller mean squared error than competing estimators. A real example is presented and analysed.     

The influence of governance on public sector efficiency: A cross-country analysis

This paper examines whether governance quality affects public sector efficiency in the policy areas of administration, education, infrastructure, and stability. Using cross-country evidence, we find that a country's measures of governance quality are positively and significantly associated with public sector efficiency in the policy areas of administration, infrastructure, and stability. However, regression results suggest that a country's governance quality cannot affect efficiency in the policy area of education, even after controlling for some explanatory variables.