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On the Bayesian estimation for the stationary Neyman-Scott point processes

Jiří Kopecký, Tomáš Mrkvička (2016)

Applications of Mathematics

The pure and modified Bayesian methods are applied to the estimation of parameters of the Neyman-Scott point process. Their performance is compared to the fast, simulation-free methods via extensive simulation study. Our modified Bayesian method is found to be on average 2.8 times more accurate than the fast methods in the relative mean square errors of the point estimates, where the average is taken over all studied cases. The pure Bayesian method is found to be approximately as good as the fast...

On the Behrens-Fisher distribution and its generalization to the pairwise comparisons

Viktor Witkovský (2002)

Discussiones Mathematicae Probability and Statistics

Weerahandi (1995b) suggested a generalization of the Fisher's solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. In this paper, we present a brief outline of the Fisher's solution and its generalization as well as the methods to calculate the p-values required for deriving the conservative joint confidence interval estimates for the pairwise mean differences, refered to as the generalized Scheffé intervals....

On the compound Poisson-gamma distribution

Christopher Withers, Saralees Nadarajah (2011)

Kybernetika

The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.

On the compound α(t)-modified Poisson distribution

Katarzyna Steliga, Dominik Szynal (2015)

Applicationes Mathematicae

In this paper we introduce compound α(t)-modified Poisson distributions. We obtain the compound Delaporte distribution as the special case of the compound α(t)-modified Poisson distribution. The characteristics of α(t)-modified Poisson and some compound distributions with gamma, exponential and Panjer summands are presented.

On the computation of the exact distribution of power divergence test statistics

Marco A. Marhuenda, Yolanda Marhuenda, Domingo Morales (2003)

Kybernetika

In this paper we introduce several algorithms to generate all the vectors in the support of a multinomial distribution. Computational studies are carried out to analyze their efficiency with respect to the CPU time and to calculate their efficiency frontiers. The proposed algorithm is used to calculate exact distributions of power divergence test statistics under the hypothesis of uniformity. Finally, several exact power comparisons are done for different divergence statistics and families of alternatives...

On the connection between cherry-tree copulas and truncated R-vine copulas

Edith Kovács, Tamás Szántai (2017)

Kybernetika

Vine copulas are a flexible way for modeling dependences using only pair-copulas as building blocks. However if the number of variables grows the problem gets fastly intractable. For dealing with this problem Brechmann at al. proposed the truncated R-vine copulas. The truncated R-vine copula has the very useful property that it can be constructed by using only pair-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this...

On the consistency of sieve bootstrap prediction intervals for stationary time series

Roman Różański, Adam Zagdański (2004)

Discussiones Mathematicae Probability and Statistics

In the article, we consider construction of prediction intervals for stationary time series using Bühlmann's [8], [9] sieve bootstrapapproach. Basic theoretical properties concerning consistency are proved. We extend the results obtained earlier by Stine [21], Masarotto and Grigoletto [13] for an autoregressive time series of finite order to the rich class of linear and invertible stationary models. Finite sample performance of the constructed intervals is investigated by computer simulations.

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