ESTIMATION OF MULTIVARIATE SHANNON ENTROPY USING MOMENTS

Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assumption that only the moments of the underlying distribution are available, a non‐traditional estimator of the entropy is suggested. We also study the practical performances of the constructed estimators through simulation studies and compare the estimators based on the moment‐recovered approaches with their counterparts derived by using the histogram and k th nearest neighbour constructions. In addition, one worked example is briefly discussed.     

Epsilon Birnbaum–Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum–Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427–443, 2005). The extension allows generating Birnbaun–Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88–95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.     

Four tests of fit for the beta-binomial distribution

Tests based on the Anderson–Darling statistic, a third moment statistic and the classical Pearson–Fisher X ² statistic, along with its third-order component, are considered. A small critical value and power study are given. Some examples illustrate important applications.     

MAXIMUM LIKELIHOOD ESTIMATION FOR A POISSON RATE PARAMETER WITH MISCLASSIFIED COUNTS

This paper proposes a Poisson‐based model that uses both error‐free data and error‐prone data subject to misclassification in the form of false‐negative and false‐positive counts. It derives maximum likelihood estimators (MLEs) for the Poisson rate parameter and the two misclassification parameters — the false‐negative parameter and the false‐positive parameter. It also derives expressions for the information matrix and the asymptotic variances of the MLE for the rate parameter, the MLE for the false‐positive parameter, and the MLE for the false‐negative parameter. Using these expressions the paper analyses the value of the fallible data. It studies characteristics of the new double‐sampling rate estimator via a simulation experiment and applies the new MLE estimators and confidence intervals to a real dataset.     

MORE INFORMATIVE TESTING FOR BIVARIATE SYMMETRY

In testing for bivariate symmetry against arbitrary alternatives the well‐known test developed by Bowker in 1948 is shown to be a score test, and to have useful components. These components are asymptotically independent and asymptotically have the standard normal distribution. Moreover they assess particular pairs of cells for symmetry. These components can also be used in a data analytic manner to complement a test for bivariate symmetry against ordered alternatives.     

Bayesian sample-size determination for one and two Poisson rate parameters with applications to quality control

We formulate Bayesian approaches to the problems of determining the required sample size for Bayesian interval estimators of a predetermined length for a single Poisson rate, for the difference between two Poisson rates, and for the ratio of two Poisson rates. We demonstrate the efficacy of our Bayesian-based sample-size determination method with two real-data quality-control examples and compare the results to frequentist sample-size determination methods.     

A further examination of antecedents of correctional staff life satisfaction

Working in corrections is not only a demanding job, but a socially important one. While a growing number of studies have examined how the work environment impacts the job stress, job satisfaction, and organizational commitment of staff, very few studies have examined how working in corrections impacts the life satisfaction of workers. The current study utilized OLS regression to examine the antecedents of life satisfaction among staff at a Midwestern private prison. Job satisfaction had a positive relationship with life satisfaction, while age, work on family conflict, family on work conflict, and job involvement all had statistically significant negative effects. Finally, perceptions of the level of financial rewards, job stress, organizational commitment, gender, race, educational level, tenure, supervisory status, position, marital status, and having children, all had non-significant associations with overall satisfaction with life.     

Subjective Versus Objective Definitions of Homelessness: Are there Differences in Risk Factors among Heavy-Drinking Women?

Investigations with homeless populations have focused on those living on the streets or in shelters; few have examined phenomena based on respondents’ self-definitions as homeless or not. This investigation examined similarities and differences among risk factors (including mental health, substance abuse, religion/spirituality, social support, and risky sexual behaviors) using two definitions of homelessness: one where place of residence defined individuals as homeless (the ‘objective’ or traditional, definition) and another where respondents defined themselves as homeless (the ‘subjective’ definition). Data come from the baseline survey of the NIAAA-funded “Sister-to-Sister” study (n = 339) of heavy-drinking women. Subjectively defined homelessness was associated with higher rates of mental health and substance use disorders, lower rates of condom use, higher rates of trading sex for food, and less social support. Objectively defined homelessness was associated with higher rates of drinking in abandoned buildings, on the streets, and in public restrooms, more new sexual partners, and higher rates of trading sex for heroin and speedballs. Investigations failing to ask for subjective information may misattribute some factors to homelessness which may overestimate the effect of various factors on homelessness. Investigators should ask respondents to define their homelessness, or they lose an important dimension of the concept of homelessness.