On evaluation of some two-dimensional normal probabilities
On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities
Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing gaussian laws may produce a potential with multiple deep wells. We study in the present work fine properties of mixtures with respect to concentration of measure and Sobolev type functional inequalities. We provide sharp Laplace bounds for Lipschitz functions in the case of generic mixtures, involving a transportation cost diameter of the mixed...
On formulae for central moments of counting distributions
The aim of this article is to give new formulae for central moments of the binomial, negative binomial, Poisson and logarithmic distributions. We show that they can also be derived from the known recurrence formulae for those moments. Central moments for distributions of the Panjer class are also studied. We expect our formulae to be useful in many applications.
On functional measures of skewness
We introduce a concept of functional measures of skewness which can be used in a wider context than some classical measures of asymmetry. The Hotelling and Solomons theorem is generalized.
On structural approximating multivariate discrete probability distributions
On the Linear Combinations of Stochastic Variables.
On the Numerical Evaluation of a Sum Involving Binomial Coefficients.
On the product of triangular random variables
We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.
On the quadratic derivative of exponential probabilities
In the paper it is shown that exponential families of probabilities have the quadratic derivative of the likelihood ratio, and explicit formulas for this derivative are derived.
On the use of difference of two proportions
Differences of two proportions occur most frequently in biomedical research. However, as far as published work is concerned, only approximations have been used to study the distribution of such differences. In this note, we derive the exact probability distribution of the difference of two proportions for seven flexible beta type distributions. The expressions involve several well known special functions. The use of these results with respect to known approximations is illustrated.