Search results for "Binomial Distribution"
showing 8 items of 28 documents
A generalization of the Binomial distribution based on the dependence ratio
2014
We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper–Haseman's Cor…
A matrix-valued Bernoulli distribution
2006
AbstractMatrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.
Efficient Simulation of Multivariate Binomial and Poisson Distributions
1998
Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the mult…
Bayesian Modeling of Sequential Discoveries
2022
We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects. We propose a novel Bayesian method for species sampling modelling by directly specifying the probability of a new discovery, therefore allowing for flexible specifications. The asymptotic behavior and finite sample properties of such an approach are extensively studied. Interestingly, our enlarged class of sequential processes includes highly tr…
Copulation duration, but not paternity share, potentially mediates inbreeding avoidance in Drosophila montana
2014
Studying the incidence of inbreeding avoidance is important for understanding the evolution of mating systems, especially in the context of mate choice for genetic compatibility. We investigated whether inbreeding avoidance mechanisms have evolved in the malt fly, Drosophila montana, by measuring mating latency (a measure of male attractiveness), copulation duration, days to remating, offspring production, and the proportion of offspring sired by the first (P1) and second (P2) male to mate in full-sibling and unrelated pairs. SNP markers were used for paternity analysis and for calculating pairwise relatedness values (genotype sharing) between mating pairs. We found 18 % inbreeding depressi…
Natural induction: An objective bayesian approach
2009
The statistical analysis of a sample taken from a finite population is a classic problem for which no generally accepted objective Bayesian results seem to exist. Bayesian solutions to this problem may be very sensitive to the choice of the prior, and there is no consensus as to the appropriate prior to use.
Correlating heatwaves and relative humidity with suicide (fatal intentional self-harm)
2021
AbstractEmpirical evidence suggests that the effects of anthropogenic climate change, and heat in particular, could have a significant impact on mental health. This article investigates the correlation between heatwaves and/or relative humidity and suicide (fatal intentional self-harm) on a global scale. The covariance between heat/humidity and suicide was modelled using a negative binomial Poisson regression with data from 60 countries between 1979–2016. Statistically significant increases and decreases in suicide were found, as well as many cases with no significant correlation. We found that relative humidity showed a more significant correlation with suicide compared to heatwaves and th…
Truncation, Information, and the Coefficient of Variation
1989
The Fisher information in a random sample from the truncated version of a distribution that belongs to an exponential family is compared with the Fisher information in a random sample from the un- truncated distribution. Conditions under which there is more information in the selection sample are given. Examples involving the normal and gamma distributions with various selection sets, and the zero-truncated binomial, Poisson, and negative binomial distributions are discussed. A property pertaining to the coefficient of variation of certain discrete distributions on the non-negative integers is introduced and shown to be satisfied by all binomial, Poisson, and negative binomial distributions.