On Comparison of Stopping Times in Sequential Procedures for Exponential Families of Stochastic Processes

For curved ( k + 1), k -exponential families of stochastic processes a natural and often studied sequential procedure is to stop observation when a linear combination of the coordinates of the canonical process crosses a prescribed level. For such procedures the model is, approximately or exactly, a non-curved exponential family. Subfamilies of these stopping rules defined by having the same Fisher (expected) information are considered. Within a subfamily the Bartlett correction for a point hypothesis is also constant. Methods for comparing the durations of the sampling periods for the stopping rules in such a subfamily are discussed. It turns out that some stopping times tend to be smaller than others. For exponential families of diffusions and of counting processes the probability that one such stopping time is smaller than another can be given explicity. More generally, an Edgeworth expansion of this probability is given     

Optimum constant-stress life test plans for Pareto distribution under type-I censoring

The paper considers the case of constant-stress partially accelerated life testing (CSPALT) when two stress levels are involved under type-I censoring. The lifetimes of test items are assumed to follow a two-parameter Pareto lifetime distribution. Maximum-likelihood method is used to estimate the parameters of CSPALT model. Confidence intervals for the model parameters are constructed. Optimum CSPALT plans that determine the best choice of the proportion of test units allocated to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance of the maximum-likelihood estimators of the model parameters. For illustration, Monte Carlo simulation studies are presented.     

The Effectiveness of Fisher’s Rebuilding Group Intervention on Divorce Adjustment and General Health of Iranian Divorced Women

This research explores the effects of participating in the Rebuilding Seminar on postdivorce adjustment and the general health of divorced women in Arak, Iran. For this quasi-experimental study, 15 participants were recruited through convenience sampling. Prior to the participation in group intervention, participants were asked to complete a demographic questionnaire, the Fisher Divorce Adjustment Scale (FDAS), and the General Health Questionnaire (GHQ–28). Participants then completed the 10 weekly, 2-hour group intervention program. After the completion of the group intervention, postintervention questionnaires were administered. Results indicate that this particular educational program affected adjustment in participants on all subscales of the FDAS, except for social self-worth. The results also suggest that the intervention program was effective on all subscales of the GHQ–28, except for somatic symptoms. Due to numerous changes in the life of divorced women and the stressful nature of divorce, designing and implementing effective intervention plans seems necessary and constructive.     

Likelihood inference for Type I bivariate Pólya–Aeppli distribution

This article discusses likelihood inference for the Type I bivariate Pólya–Aeppli distribution. The Type I bivariate Pólya–Aeppli distribution was derived by Minkova and Balakrishnan by using compounding with geometric random variables and the trivariate reduction method. They also discussed the moment estimation of the parameters of the Type I bivariate Pólya–Aeppli distribution. Here, we carry out a simulation study to compare the performance of the developed Maximum Likelihood Estimation (MLE) method with the moment estimation. The obtained results show that, through the MLEs require more computational time compared to the moment estimates (MoM), the MLEs perform better, in most of the settings, than the MoM. Finally, we apply the Type I bivariate Pólya–Aeppli model to a real dataset containing the frequencies of railway accidents in two subsequent six-year periods for the purpose of illustration. We also carry out some hypothesis tests using the Wald test statistic. From these results, we conclude that the two variables belong to the same univariate Pólya–Aeppli distribution, but are correlated.     

Exact distribution of a modified Behrens–Fisher statistic

The exact distribution of a modified Behrens–Fisher statistic is derived. The distribution function is mostly elementary and is simpler than the exact distribution derived by Nel et al. Its practical use (including computationalefficiency and computational convenience) is discussed.     

Lifetime performance index based on ranked set sampling

In this article, we assume that the lifetimes of products follow a one-parameter exponential distribution and use both conjugate and Jeffreys prior distributions for finding a Bayes estimator based on the RSS scheme for lifetime performance index CL. We also obtained maximum likelihood and adhac estimators for CL. Monte Carlo simulation study is done for comparing the obtained estimators in two sampling schemes SRS and RSS. Fisher information has been utilized to obtain lower confidence bound of CL for both schemes in asymptotically state and use this bounds for hypothesis testing of CL.     

Properties of the elasticity of a continuous random variable. A special look at its behavior and speed of change

Belzunce et al. (1995 Belzunce, F., Candel, J., Ruiz, J.M. (1995). Ordering of truncated distributions through concentration curves. Sankhya 57:375–383. [Google Scholar]) define the elasticity for non negative random variables as the reversed proportional failure rate (RPFR). Veres-Ferrer and Pavía (2012 Veres-Ferrer, E.J., Pavía, J.M. (2012). La elasticidad: una nueva herramienta para caracterizar distribuciones de probabilidad. Rect@ 13:145–158. [Google Scholar], 2014b Veres-Ferrer, E.J., Pavía, J.M. (2014b). On the relationship between the reversed hazard rate and elasticity. Stat. Pap. 55:275–284.[Crossref], [Web of Science ®] , [Google Scholar]) interpret it in economic terms, extending its definition to variables that can also take negative values, and briefly present the role of elasticity in characterizing probability distributions. This paper highlights a set of properties demonstrated by elasticity, which shows many similar properties to the reverse hazard function. This paper pays particular attention to studying the increase/decrease and the speed of change of the elasticity function. These are important properties because of the characterizing role of elasticity, which makes it possible to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way. As a general rule, it is observed the need for distinguishing between positive and negative areas of the support.     

A unified framework for analysis and comparison of randomized response surveys of binary characteristics

The randomized response (RR) procedures for estimating the proportion (π)$(\pi )$ of a population belonging to a sensitive or stigmatized group ask each respondent to report a response by randomly transforming his/her true attribute into one of several response categories. In this paper, we present a common framework for discussing various RR surveys of dichotomous populations with polychotomous responses. The unified approach is focused on the substantive issues relating to respondents’ privacy and statistical efficiency and is helpful for fair comparison of various procedures. We describe a general technique for constructing unbiased estimators of π$\pi$ based on arbitrary RR procedures, from unbiased estimators based on an open survey with the same sampling design. The technique works well for any sampling design p(s)$p(s)$ and also for variance estimation. We develop an approach for comparing RR procedures, taking both respondents’ protection and statistical efficiency into account. For any given RR procedure with three or more response categories, we present a method for designing an RR procedure with a binary response variable which provides the same respondents’ protection and at least as much statistical information. This result suggests that RR surveys of dichotomous populations should use only binary response variables.     

Sir Godfrey Thomson: a statistical pioneer

Summary.  Godfrey Thomson (1881–1955) was a leading figure in intelligence testing who made his name in that field first at Armstrong College, Newcastle, and then at the University of Edinburgh. In the course of his practical work he identified many theoretical problems which were essentially statistical in character. In particular, he used maximum likelihood estimation as early as 1919 and his statistical work largely set the course of modern factor analysis and related techniques. His statistical abilities were recognized, at different stages of his career, by both Karl Pearson and Sir Ronald Fisher. His key insight was to recognize the importance of Fisherian inference for the future of that subject.     

Conditional optimal spacing in exponential distribution

In this paper, we propose the conditional optimal spacing defined as the optimal spacing after specifying a predetermined order statistic. If we specify a censoring time, then the optimal inspection times for grouped inspection can be determined from this conditional optimal spacing. We take an example of exponential distribution, and provide a simple method of finding the conditional optimal spacing.