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 2

Displaying 21 – 35 of 35

Showing per page

Exact distribution under independence of the diagonal section of the empirical copula

Arturo Erdely, José M. González–Barrios (2008)

Kybernetika

In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three- dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2].

Exact laws for sums of ratios of order statistics from the Pareto distribution

André Adler (2006)

Open Mathematics

Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).

Expansions for the distribution of M-estimates with applications to the Multi-Tone problem

Christopher S. Withers, Saralees Nadarajah (2011)

ESAIM: Probability and Statistics

We give a stochastic expansion for estimates θ ^ that minimise the arithmetic mean of (typically independent) random functions of a known parameterθ. Examples include least squares estimates, maximum likelihood estimates and more generally M-estimates. This is used to obtain leading cumulant coefficients of θ ^ needed for the Edgeworth expansions for the distribution and densityn1/2θ0) to magnitude n−3/2 (or to n−2 for the symmetric case), where θ0 is the true parameter value and n is typically the...

Expansions for the distribution of M-estimates with applications to the Multi-Tone problem

Christopher S. Withers, Saralees Nadarajah (2012)

ESAIM: Probability and Statistics

We give a stochastic expansion for estimates that minimise the arithmetic mean of (typically independent) random functions of a known parameter θ. Examples include least squares estimates, maximum likelihood estimates and more generally M-estimates. This is used to obtain leading cumulant coefficients of needed for the Edgeworth expansions for the distribution and density n1/2 ( of − θ0) to magnitude n−3/2 (or to n−2 for the symmetric case), where θ0 is the true parameter value and n is typically...

Exploiting tensor rank-one decomposition in probabilistic inference

Petr Savický, Jiří Vomlel (2007)

Kybernetika

We propose a new additive decomposition of probability tables – tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one- dimensional tables. Entries in tables are allowed to be any real number, i. e. they can be also negative numbers. The possibility of having...

Exponential deficiency of convolutions of densities

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

If a probability density p(x) (x ∈ ℝk) is bounded and R(t) := ∫e〈x, tu〉p(x)dx &lt; ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density p ˜ t ˜pt := e〈x, tu〉p(x)/R(t) is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...

Exponential deficiency of convolutions of densities∗

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

If a probability density p(x) (x ∈ ℝk) is bounded and R(t) := ∫e〈x, tu〉p(x)dx < ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density p ˜ t := e〈x, tu〉p(x)/R(t) is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...

Extremal and additive processes generated by Pareto distributed random vectors

Kosto V. Mitov, Saralees Nadarajah (2014)

ESAIM: Probability and Statistics

Pareto distributions are most popular for modeling heavy tailed data. Here, we obtain weak limits of a sequence of extremal and a sequence of additive processes constructed by a series of Bernoulli point processes with bivariate Pareto space components. For the limiting processes we derive the one dimensional distributions in explicit forms. Some of the main properties of these distributions are also proved.

Extreme distribution functions of copulas

Manuel Úbeda-Flores (2008)

Kybernetika

In this paper we study some properties of the distribution function of the random variable C(X,Y) when the copula of the random pair (X,Y) is M (respectively, W) – the copula for which each of X and Y is almost surely an increasing (respectively, decreasing) function of the other –, and C is any copula. We also study the distribution functions of M(X,Y) and W(X,Y) given that the joint distribution function of the random variables X and Y is any copula.

Extreme order statistics in an equally correlated Gaussian array

Mateusz Wiśniewski (1994)

Applicationes Mathematicae

This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given.

Currently displaying 21 – 35 of 35

Previous Page 2