The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 23 Next

Displaying 441 – 460 of 656

Showing per page

On the Lukacs property for free random variables

Kamil Szpojankowski (2015)

Studia Mathematica

The Lukacs property of the free Poisson distribution is studied. We prove that if free and are free Poisson distributed with suitable parameters, then + and ( + ) - 1 / 2 ( + ) - 1 / 2 are free. As an auxiliary result we compute the joint cumulants of and - 1 for free Poisson distributed . We also study the Lukacs property of the free Gamma distribution.

On the Mathematical Theory of Records

Alexei Stepanov (2021)

Communications in Mathematics

In the present work, we briefly analyze the development of the mathematical theory of records. We first consider applications associated with records. We then view distributional and limit results for record values and times. We further present methods of generation of continuous records. In the end of this work, we discuss some tests based on records.

On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments

Dietmar Ferger (2005)

ESAIM: Probability and Statistics

Let F n be the empirical distribution function (df) pertaining to independent random variables with continuous df F . We investigate the minimizing point τ ^ n of the empirical process F n - F 0 , where F 0 is another df which differs from F . If F and F 0 are locally Hölder-continuous of order α at a point τ our main result states that n 1 / α ( τ ^ n - τ ) converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...

On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments

Dietmar Ferger (2010)

ESAIM: Probability and Statistics

Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point τ ^ n of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that n 1 / α ( τ ^ n - τ ) converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...

On the Newcomb-Benford law in models of statistical data.

Tomás Hobza, Igor Vajda (2001)

Revista Matemática Complutense

We consider positive real valued random data X with the decadic representation X = Σi=∞∞Di 10i and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = Di ≥ 1, Di+1 = Di+2 = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log10(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with log10X uniformly distributed on an interval (m,n) where m and n are integers. We show that if log10X has a distribution function...

On the optimal continuous experimental design problem

Christos P. Kitsos (2011)

Discussiones Mathematicae Probability and Statistics

The target of this paper is to provide a compact review of the Optimal Experimental Design, the continuous case. Therefore we are referring to the general nonlinear problem in comparison to the linear one.

On the optimal number of classes in the Pearson goodness-of-fit tests

Domingo Morales, Leandro Pardo, Igor Vajda (2005)

Kybernetika

An asymptotic local power of Pearson chi-squared tests is considered, based on convex mixtures of the null densities with fixed alternative densities when the mixtures tend to the null densities for sample sizes n → ∞ . This local power is used to compare the tests with fixed partitions 𝒫 of the observation space of small partition sizes | 𝒫 | with the tests whose partitions 𝒫 = 𝒫 n depend on n and the partition sizes | 𝒫 n | tend to infinity for n → ∞ . New conditions are presented under which it is asymptotically optimal...

Currently displaying 441 – 460 of 656