Search results for "Binomial Distribution"
showing 10 items of 28 documents
A Modification of Stone's Test for Trend for Binary Outcome
1998
STONE (1988) suggested the first isotonic regression estimator as a tool for drawing inferences on possibly increased cancer case counts among several subregions around a putative source. He assumed the case counts to be Poisson distributed and therefore introduced a rare disease assumption into his approach. However, when analyzing cross sectional data one would rather refer to prevalence estimates among these subregions around a point risk source (for example the origin of chemical fallout). Therefore we applied antitonic regression estimation in Binomial distributions to derive a test statistic and a p value to test for a possible trend in the observed prevalence data around the putative…
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.
An alternative representation of Altham's multiplicative-binomial distribution
1998
Abstract Cox (1972) introduced a log-linear representation for the joint distribution of n binary-dependent responses. Altham (1978) derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox's representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.
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…
Occlusion-based estimation of independent multinomial random variables using occurrence and sequential information
2017
Abstract This paper deals with the relatively new field of sequence-based estimation in which the goal is to estimate the parameters of a distribution by utilizing both the information in the observations and in their sequence of appearance. Traditionally, the Maximum Likelihood (ML) and Bayesian estimation paradigms work within the model that the data, from which the parameters are to be estimated, is known, and that it is treated as a set rather than as a sequence. The position that we take is that these methods ignore, and thus discard, valuable sequence -based information, and our intention is to obtain ML estimates by “extracting” the information contained in the observations when perc…
Comparison of the Andersen–Gill model with poisson and negative binomial regression on recurrent event data
2008
Many generalizations of the Cox proportional hazard method have been elaborated to analyse recurrent event data. The Andersen-Gill model was proposed to handle event data following Poisson processes. This method is compared with non-survival approaches, such as Poisson and negative binomial regression. The comparison is performed on data simulated according to various event-generating processes and differing in subject heterogeneity. When robust standard error estimates are applied, for Poisson processes the Andersen-Gill approach is comparable to a negative binomial regression, whereas the poisson regression has comparable coverage probabilities of confidence intervals, but increased type …
The Random-Time Binomial Model
1999
In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence of the values for European and American put options. Differently to the CRR-model the convergence behaviour is extremely smooth in our model. By using extrapolation we therefore achieve order of convergence two. This way it is an efficient tool for pricing purposes in the Black-Scholes setup, since the CRR model and its extrapolations typically achieve order one. Moreover our model allows in a straig…
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…
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.
Objective Priors for Discrete Parameter Spaces
2012
This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the reference prior approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain types of structure. To take advantage of structure, this article proposes embedding the original problem in a continuous problem that preserves the structure, and then using standard reference prior theory to determine the appropriate objective prior. Four different possibilities for this embedding are explored, and applied to a population-size model, the hypergeometric distribution, the multivariate hy…