Probability-generating function

About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.

Minimum distance estimators for count data based on the probability generating function with applications

Abstract: This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specifically, it is shown that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, asymptotically normal. These properties hold even if the model is misspecified. Three applications of the obtained results are considered. First, we revisit the goodness-of-fit problem for count data and propose a weighted bootstrap estimator of the null distribution of test statistics based on the above cited distance. Second, we give a probability generating function version of the model selection test problem for separate, overlapping and nested families of distributions. Finally, we provide an application to the problem of testing for separate families of distributions. All applications are illustrated with numerical examples.

Method, computer program, and storage medium for estimating randomness of function of representative value of random variable by the use of gradient of same function

Abstract: A method of estimating a measure of randomness of a function of at least one representative value of at least one random variable is constructed to have the steps of obtaining the at least one random variable; determining the at least one representative value of the obtained at least one random variable; determining a first statistic of the obtained at least one random variable; determining a gradient of the function with respect to the determined at least one representative value; and transforming the obtained first statistic into a second statistic of the function, using the determined gradient The step of transforming may be adapted to transform the first statistic into the second statistic, such that the second statistic responds to the first statistic more sensitively in the case of the gradient being steep than in the case of the gradient being gentle

Probability and Random Variables

Abstract: Probability Conditional probability and independence Random variables Continuous distributions Distribution function Functions of random variables Bivariate distributions Expectation of a random variable Variance of a random variable Moment generating functions Moments of bivariate distributions Probability generating functions Sums of random variables Unbiased estimators Sampling finite populations Generating random variables.