When overdispersion and correlation co-occur in longitudinal count data, as is often the case, an analysis method that can handle both phenomena simultaneously is needed. The correlated Poisson distribution (CPD) proposed by Drezner and Farnum (Communications in Statistics-Theory and Methods, 22(11), 3051–3063, 1994) is a generalization of the classical Poisson distribution with the incorporation of an additional parameter that allows dependence between successive observations of the phenomenon under study. This parameter both measures the correlation and reflects the degree of dispersion. The classical Poisson distribution is obtained as a special case when the correlation is zero. We present an in-depth review of this CPD and discuss some methods to estimate the distribution parameters. The inclusion of regression components in this distribution is enabled by allowing one of the parameters to include available information concerning, in this case, automobile insurance policyholders. The proposed distribution can be viewed as an alternative to the Poisson, negative binomial, and Poisson-inverse Gaussian approaches. We then describe applications of the distribution, suggest it is appropriate for modeling the number of claims in an automobile insurance portfolio, and establish some new distribution properties.

The impact of macroparasites on their hosts is proportional to the number of parasites per host, or parasite abundance. Abundance values are count data, i.e. integers ranging from 0 to some maximum number, depending on the host–parasite system. When using parasite abundance as a predictor in statistical analysis, a common approach is to bin values, i.e. group hosts into infection categories based on abundance, and test for differences in some response variable (e.g. a host trait) among these categories. There are well-documented pitfalls associated with this approach. Here, I use a literature review to show that binning abundance values for analysis has been used in one-third of studies published in parasitological journals over the past 15 years, and half of the studies in ecological and behavioural journals, often without any justification. Binning abundance data into arbitrary categories has been much more common among studies using experimental infections than among those using naturally infected hosts. I then use simulated data to demonstrate that true and significant relationships between parasite abundance and host traits can be missed when abundance values are binned for analysis, and vice versa that when there is no underlying relationship between abundance and host traits, analysis of binned data can create a spurious one. This holds regardless of the prevalence of infection or the level of parasite aggregation in a host sample. These findings argue strongly for the practice of binning abundance data as a predictor variable to be abandoned in favour of more appropriate analytical approaches.

We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

In the present technological age, where cyber-risk ranks alongside natural and man-made disasters and catastrophes – in terms of global economic loss – businesses and insurers alike are grappling with fundamental risk management issues concerning the quantification of cyber-risk, and the dilemma as to how best to mitigate this risk. To this end, the present research deals with data, analysis, and models with the aim of quantifying and understanding cyber-risk – often described as “holy grail” territory in the realm of cyber-insurance and IT security. Nonparametric severity models associated with cyber-related loss data – identified from several competing sources – and accompanying parametric large-loss components, are determined, and examined. Ultimately, in the context of analogous cyber-coverage, cyber-risk is quantified through various types and levels of risk adjustment for (pure-risk) increased limit factors, based on applications of actuarially founded aggregate loss models in the presence of various forms of correlation. By doing so, insight is gained into the nature and distribution of volatile severity risk, correlated aggregate loss, and associated pure-risk limit factors.

Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a confidence interval having the desired width is examined. A two-stage approximation to the sample size requirement is shown to give accurate results.

Corrections of correlations for range restriction (i.e., selection) and unreliability are common in psychometric work. The current rule of thumb for determining the order in which to apply these corrections looks to the nature of the reliability estimate (i.e., restricted or unrestricted). While intuitive, this rule of thumb is untenable when the correction includes the variable upon which selection is made, as is generally the case. Using classical test theory, we show that it is the nature of the range restriction, not the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability.

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.

Using variance stabilizing transformations, this note describes approximate solutions to the ranking and selection problem of selecting the best binomial population or the bivariate normal population with the largest correlation coefficient.

The validity of a test is often estimated in a nonrandom sample of selected individuals. To accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction. Unfortunately, this corrected correlation cannot be transformed using Fisher's Z transformation, and asymptotic tests of hypotheses based on small or moderate samples are not accurate. We developed a Fisher r to Z transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on the predictor (the missing data were MAR); and (b) the criterion was missing at random, not due to selection (the missing data were MCAR). The two Z transformations were evaluated in a computer simulation. The transformations were accurate, and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations.

The scoring of response vectors to give maximum test-retest correlation is investigated. Simple sufficiency arguments show that the form of the best scores is very restricted. A general method is given for finding the best scores, deriving the best scores for the normal factor model, and showing by calculation of several particular cases that for a standard model for binary response it is easy to approximate the best scores.

We derive an analytic model of the inter-judge correlation as a function of five underlying parameters. Inter-cue correlation and the number of cues capture our assumptions about the environment, while differentiations between cues, the weights attached to the cues, and (un)reliability describe assumptions about the judges. We study the relative importance of, and interrelations between these five factors with respect to inter-judge correlation. Results highlight the centrality of the inter-cue correlation. We test the model’s predictions with empirical data and illustrate its relevance. For example, we show that, typically, additional judges increase efficacy at a greater rate than additional cues.