Displaying similar documents to “Optimal nonlinear transformations of random variables”

Computing the distribution of a linear combination of inverted gamma variables

Viktor Witkovský (2001)

Kybernetika

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A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized p -values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced...

Nonparametric estimations of non-negative random variables distributions

František Vávra, Pavel Nový, Hana Mašková, Michala Kotlíková, David Zmrhal (2003)

Kybernetika

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The problem of estimation of distribution functions or fractiles of non- negative random variables often occurs in the tasks of risk evaluation. There are many parametric models, however sometimes we need to know also some information about the shape and the type of the distribution. Unfortunately, classical approaches based on kernel approximations with a symmetric kernel do not give any guarantee of non-negativity for the low number of observations. In this note a heuristic approach,...

Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test.

Mikhail S. Nikulin, Vassiliy G. Voinov (1993)

Qüestiió

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We consider the problem of estimation of the value of a real-valued function u(θ), θ = (θ, ..., θ), on the basis of a sample from non-truncated or truncated multivariate Modified Power Series Distributions. Using the general theory of estimation and the results of Patil (1965) and Patel (1978) we give the tables of MVUE's for functions of parameter θ of trinomial, multinomial, negative-multinomial and left-truncated modified power series distributions. We have applied the properties...

Minimax prediction under random sample size

Alicja Jokiel-Rokita (2002)

Applicationes Mathematicae

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A class of minimax predictors of random variables with multinomial or multivariate hypergeometric distribution is determined in the case when the sample size is assumed to be a random variable with an unknown distribution. It is also proved that the usual predictors, which are minimax when the sample size is fixed, are not minimax, but they remain admissible when the sample size is an ancillary statistic with unknown distribution.