The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal distribution. Although the sum tends eventually to a Gaussian distribution, the distribution of the sum is always close to a log-normal distribution rather t...

Distribution of a quantity, e.g., concentration of a serum constituent, in a typical general hospital population is considered. It is assumed that the distribution within any subpopulation is Gaussian and that adjacent subpopulations overlap somewhat, presenting overlapping Gaussian distri butions. Bhattacharya’s procedure for resolving such overlapping distributions, based upon differentiation...

Michael, Schucany & Haas (1976) presented a method for the simulation of random variates using transformations with multiple roots. A generalization of this method to include vectorvalued transformations is given here. A short introduction to the inverse Gaussian distribution is given. The joint distribution of the sufficient statistic is well known, but the proof given here based on the Basu t...

We show that the distribution of the sizes and temperatures of clusters can be used to constrain cosmological models. The size-temperature (ST) distribution predicted in a flat Gaussian cluster-abundance-normalized Ω0 = 0.3 model agrees well with the fairly tight ST relation observed. A larger power-spectrum amplitude σ8 would give rise to a larger scatter about the ST relation as would a large...

The efficiency of many speech processing methods rely on accurate modeling of the distribution of the signal spectrum and a majority of prior works suggest that the spectral components follow the Laplace distribution. To improve the probability distribution models based on our knowledge of speech source modeling, we argue that the model should in fact be a multiplicative mixture model, includin...

Probabilistic range query is an important type of query in the area of uncertain data management. A probabilistic range query returns all the data objects within a specific range from the query object with a probability no less than a given threshold. In this paper, we assume that each uncertain object stored in the database is associated with a multi-dimensional Gaussian distribution, which de...

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback...