Search results for "Binomial Distribution"
showing 10 items of 28 documents
The best fit for the observed galaxy Counts-in-Cell distribution function
2017
The Sloan Digital Sky Survey (SDSS) is the first dense redshift survey encompassing a volume large enough to find the best analytic probability density function that fits the galaxy Counts-in-Cells distribution $f_V(N)$, the frequency distribution of galaxy counts in a volume $V$. Different analytic functions have been previously proposed that can account for some of the observed features of the observed frequency counts, but fail to provide an overall good fit to this important statistical descriptor of the galaxy large-scale distribution. Our goal is to find the probability density function that better fits the observed Counts-in-Cells distribution $f_V(N)$. We have made a systematic stud…
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…
Breeding abundance of threatened raptors as estimated from occurrence data
2008
A model derived from the negative binomial distribution (NBD) has been proposed to solve the problem of predicting abundance of species from occurrence maps. The viability of NBD was explored for predicting the breeding abundance of five threatened species of raptor: Bonelli's Eagle Hieraaetus fasciatus, Golden Eagle Aquila chrysaetos, Peregrine Falco peregrinus, Lanner Falco biarmicus and Lesser Kestrel Falco naumanni. First, the accuracy of the NBD was tested in a reference area where the species abundance and occurrence were known through intensive field surveys. Next, an estimation of regional abundance derived from NBD was made for each species. These estimates were then compared to th…
Heterogeneity of traditional and digital media use among older adults: A six-country comparison
2021
Abstract The concept of aged heterogeneity has been associated with older adults' ability to adapt to the digital age without a systematic empirical analysis. We analyse retired adults' (aged 62 or more) use of traditional media and their digital equivalents in six countries. First, we ask whether heterogeneity in traditional and digital media use increases with age. Second, we study to what extent gender is related to this heterogeneity, and third, the country differences in the heterogeneity of media use in later life. We analyse the 2018 data (N = 5865) of the ‘Older audiences in the digital media environment’ survey using zero-inflated negative binomial models. The results provide parti…
What Does Objective Mean in a Dirichlet-multinomial Process?
2017
Summary The Dirichlet-multinomial process can be seen as the generalisation of the binomial model with beta prior distribution when the number of categories is larger than two. In such a scenario, setting informative prior distributions when the number of categories is great becomes difficult, so the need for an objective approach arises. However, what does objective mean in the Dirichlet-multinomial process? To deal with this question, we study the sensitivity of the posterior distribution to the choice of an objective Dirichlet prior from those presented in the available literature. We illustrate the impact of the selection of the prior distribution in several scenarios and discuss the mo…
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 …
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.
A generalization of the Binomial distribution based on the dependence ratio
2015
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 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…
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…