A COM-Poisson-type generalization of the negative binomial distribution

ABSTRACT

This paper introduces a generalization of the negative binomial (NB) distribution in analogy with the COM-Poisson distribution. Many well-known distributions are particular and limiting distributions. The proposed distribution belongs to the modified power series, generalized hypergeometric and exponential families, and also arises as weighted NB and COM-Poisson distributions. Probability and moment recurrence formulae, and probabilistic and reliability properties have been derived. With the flexibility to model under-, equi- and over-dispersion, and its various interesting properties, this NB generalization will be a useful model for count data. An application to empirical modeling is illustrated with a real data set.     

The family formation process among U.S. marriage cohorts

The family formation process is viewed as the progression of women through first marriage, first, subsequent, and last births and is examined for differential patterns of timing in 1930–1969 marriage cohorts. Based on the childbearing histories of approximately 17,000 white women once and still married, extracted from the June 1975 Current Population Survey, the study uses a dynamic model to show the varying importance across cohorts of the first birth interval as an important indicator of the total time spent in childbearing, social background effects in differentiating the timing of the first two births, and of prior birth transitions as affecting subsequent ones.     

Evolving Perceptions of Clinical Management in Acute Hospitals in England

Clinical management is at the centre of organizational change in the contemporary British hospital sector, and throws up important questions about the relationship between medicine and management. Through the analysis of business planning as a key organizational process the interpretative frameworks which guide the perceptions of the roles of clinical directors and directorate managers can be understood. This paper presents empirical material from a study of an acute hospital trust going through a full business planning cycle, and traces the evolving interpretations of the nature, content and form of clinical management. It also provides insights into the changing face of the medical profession and its place within the health services domain.     

Fall incidence in a state psychiatric hospital in Singapore

The results of a retrospective study of fall incidence during a 1-year period in a psychiatric hospital in Singapore are reported, involving 309 patients who fell one or more times during their stay. The profile of inpatients involved in falls was identified. Data were derived from standard incident forms completed whenever patients had a fall. A total of 348 falls were identified for the 1-year period. Results revealed higher fall rates in younger male epileptic patients; elderly female patients, age 70 and older with depression or dementia; individuals with concomitant medical conditions; and patients taking three types of medication. The majority of falls occurred when the activity level was high in the ward. Young epileptic patients and elderly depressed patients were prone to repeated falls. These results have the potential to assist in identifying patients at high risk and in designing and implementing strategies to prevent such incidents.     

Variational Bayes with synthetic likelihood

Synthetic likelihood is an attractive approach to likelihood-free inference when an approximately Gaussian summary statistic for the data, informative for inference about the parameters, is available. The synthetic likelihood method derives an approximate likelihood function from a plug-in normal density estimate for the summary statistic, with plug-in mean and covariance matrix obtained by Monte Carlo simulation from the model. In this article, we develop alternatives to Markov chain Monte Carlo implementations of Bayesian synthetic likelihoods with reduced computational overheads. Our approach uses stochastic gradient variational inference methods for posterior approximation in the synthetic likelihood context, employing unbiased estimates of the log likelihood. We compare the new method with a related likelihood-free variational inference technique in the literature, while at the same time improving the implementation of that approach in a number of ways. These new algorithms are feasible to implement in situations which are challenging for conventional approximate Bayesian computation methods, in terms of the dimensionality of the parameter and summary statistic.     

Analysis of discrete data by Conway–Maxwell Poisson distribution

In this paper, we further study the Conway–Maxwell Poisson distribution having one more parameter than the Poisson distribution and compare it with the Poisson distribution with respect to some stochastic orderings used in reliability theory. Likelihood ratio test and the score test are developed to test the importance of this additional parameter. Simulation studies are carried out to examine the performance of the two tests. Two examples are presented, one showing overdispersion and the other showing underdispersion, to illustrate the procedure. It is shown that the COM-Poisson model fits better than the generalized Poisson distribution.     

“Y,what do you think about what X just said?” Conversation analysis of stance-eliciting questions in open dialogue network meetings

Open dialogue is a resource-oriented approach to mental health, which aims to help those involved in a crisis situation support each other and engage in dialogue. While language use in open dialogue is generally characterized as being open-ended, nondirective, and nonevaluating on the professionals' side, little is known about the specific conversational features. The aim of this study was to analyze the interactional functions of a stance-eliciting question of the form: “Y, what do you think about what X just said?” We used conversation analysis (CA) to examine this in eight video-recorded Danish open dialogue network meetings. In CA, stance involves expressions of attitude, affect, or judgments about people or events. We describe the interactional functions of these stance-eliciting questions and discuss how clinicians used them as a tool for accomplishing neutrality. The findings can be used to gain a more nuanced understanding of open dialogue psychotherapeutic practices.     

Parent physical punishment and child aggression in a Singapore Chinese preschool sample

We examine how parental physical punishment (caning and slapping) and child aggression are related, and possible moderation by authoritative control and rejection. A sample of 286 Singapore Chinese preschoolers ages 4–6 reported on rejection; their parents reported on control, caning, and slapping; and their teachers rated child aggression. Results show that father caning is related to aggression, regardless of child gender, whereas mother caning is related to child aggression only at low rejection. Mother slapping is related to sons’ aggression, whereas father slapping is related to daughters’ aggression only at low rejection. Control does not moderate any of the punishment‐aggression links. The punishment‐aggression link is thus a complex one, dependent on the dyad, the punitive act, and the parent's behavior.     

Statistical Analysis for the Inverse Trinomial Distribution

This article considers parameter estimation, goodness of fit, likelihood ratio and score tests, and model selection by Akaike information criterion for the inverse trinomial (IT) distribution, a classical one-dimensional random walk distribution. The IT distribution has a cubic variance function of the mean and is a generalization of the negative binomial distribution. Basic distributional properties and expressions for the probability mass function, recurrence formula, moments, and score functions are also presented.