Contents 1. Introduction 1 2. The central limit theorem 1 3. The normal approximation of the binomial distribution 2 4. The normal approximation of the mixed binomial distribution 4 5. The law of large numbers approximation of a mixed binomial distribution 6 6. Finding the mixed binomial distribution by using Monte Carlo simulations 6 6.

The purpose of this paper is to suggest a method of analyzing data from clinical mastitis trials when the response of interest is binary (success/failure) in nature, and the type of experimental design adheres to an incomplete block form. This approach is referred to as an "Empirical Bayes" strategy in statistical literature and incorporates over-dispersion commonly associated with binomial tri...

Data is everywhere, notably in this information explosion era. Beyond the first-order summary of a sample by its average value or its median, the bell-shaped Gaussian (or normal) curve has long been observed in the histograms of many data samples since the early history of probability, statistics and related fields. The Gaussian distribution, known commonly under the name of Law of Frequency of...

Small-scale artisanal fisheries can have a significant negative impact in cetacean populations. Cetacean bycatch has been documented in the pole-and-line tuna fishery in the Azores with common dolphins being the species more frequently taken. Based on data collected by observers on ∼50% of vessels operating from 1998 to 2012, we investigate the influence of various environmental and fisheries-r...

In a 1992 Technometrics paper, Lambert (1992, 34, 1-14) described zero-inflated Poisson (ZIP) regression, a class of models for count data with excess zeros. In a ZIP model, a count response variable is assumed to be distributed as a mixture of a Poisson(lambda) distribution and a distribution with point mass of one at zero, with mixing probability p. Both p and lambda are allowed to depend on ...

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probab...

The exponential distribution is also the continuous analog of the geometric distribution in the following sense. In an experiment where the binomial distribution describes the number of successes in n trials, the geometric distribution describes the number of trials necessary for one success. In an experiment where the Poisson distribution describes the number of random occurrences of some even...

This paper presents an optimal strategy for sequential sampling from binomial distributions. The strategy presented is general in that it is a "multi-action" rather than a twoaction procedure. While the major task is to estimate the proportion, p, of "successes" in a hypothetical, infinite population of binary observations, it is assumed that the decision maker is only concerned with which of a...

The Fokker-Planck equation is considered, which is connected to the birth and death process with immigration by the Poisson transform. The fractional derivative in time variable is introduced into the Fokker-Planck equation in order to investigate an origin of oscillatory behavior of cumulant moments. From its solution (the probability density function), the generating function (GF) for the cor...

OBJECTIVE To investigate the spatial distribution of Aedes albopictus population to provide input for developing sampling plans and supporting decision making on the control of this vector in field sampling. METHODS A study was carried out in an urban area that has a vestige of primary vegetation, 20 km away from Dourados, Midwestern Brazil. Ten samplings were conducted between January 28, 20...