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Binomial ARMA count series from renewal processes

Sergiy Koshkin, Yunwei Cui (2012)

Discussiones Mathematicae Probability and Statistics

This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1)...

Biquadratic functions: stationarity and invertibility in estimated time-series models.

D. S. G. Pollock (1989)

Qüestiió

It is important that the estimates of the parameters of an autoregressive moving-average (ARMA) model should satisfy the conditions of stationarity and invertibility. It can be shown that the unconditional maximum-likelihood estimates are bound to fill these conditions regardless of the size of the sample from which they are derived; and, in some quarters, it has been argued that they should be used in preference to any other estimates when the size of he sample is small. However, the maximum-likelihood...

Bivariate copulas, norms and non-exchangeability

Pier Luigi Papini (2015)

Dependence Modeling

The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.

Bivariate copulas: Transformations, asymmetry and measures of concordance

Sebastian Fuchs, Klaus D. Schmidt (2014)

Kybernetika

The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the...

Bivariate gamma distribution as a life test model

Giri S. Lingappaiah (1984)

Aplikace matematiky

The bivariate gamma distribution is taken as a life test model to analyse a series system with two dependent components x and y . First, the distribution of a function of x and y , that is, minimum ( x , y ) , is obtained. Next, the reliability of the component system is evaluated and tabulated for various values of the parameters. Estimates of the parameters are also obtained by using Bayesian approach. Finally, a table of the mean and variance of minimum ( x , y ) for various values of the parameters involved is...

Blended φ -divergences with examples

Václav Kůs (2003)

Kybernetika

Several new examples of divergences emerged in the recent literature called blended divergences. Mostly these examples are constructed by the modification or parametrization of the old well-known phi-divergences. Newly introduced parameter is often called blending parameter. In this paper we present compact theory of blended divergences which provides us with a generally applicable method for finding new classes of divergences containing any two divergences D 0 and D 1 given in advance. Several examples...

Block matrix approximation via entropy loss function

Malwina Janiszewska, Augustyn Markiewicz, Monika Mokrzycka (2020)

Applications of Mathematics

The aim of the paper is to present a procedure for the approximation of a symmetric positive definite matrix by symmetric block partitioned matrices with structured off-diagonal blocks. The entropy loss function is chosen as approximation criterion. This procedure is applied in a simulation study of the statistical problem of covariance structure identification.

Bolshev's method of confidence limit construction.

Vacys Bagdonavicius, Valentina Nikoulina, Mikhail Nikulin (1997)

Qüestiió

Confidence intervals and regions for the parameters of a distribution are constructed, following the method due to L. N. Bolshev. This construction method is illustrated with Poisson, exponential, Bernouilli, geometric, normal and other distributions depending on parameters.

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