Estimation of log-linear-binomial distribution with applications.
Estimators for epidemic alternatives
We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.
Étude des propriétés asymptotiques des estimateurs des moindres carrés pour des problèmes de régression à phases multiples
Evaluating improvements of records
We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.
Evaluating the bivariate compound generalized Poisson distribution.
Evaluations of expected generalized order statistics in various scale units
We present sharp upper bounds for the deviations of expected generalized order statistics from the population mean in various scale units generated by central absolute moments. No restrictions are imposed on the parameters of the generalized order statistics model. The results are derived by combining the unimodality property of the uniform generalized order statistics with the Moriguti and Hölder inequalities. They generalize evaluations for specific models of ordered observations.
Exact and approximate distributions for the product of Dirichlet components
It is well known that has the beta distribution when and follow the Dirichlet distribution. Linear combinations of the form have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose...
Exact distribution for the generalized F tests
Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate...
Exact distribution under independence of the diagonal section of the empirical copula
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 distributions for some Rényi-type statistics
Exact distributions in the model of a regression line for the threshold parameter with exponential distribution of errors
In this paper it is shown how one can work out exact distributions of estimators and test statistics in the model of a regression line for the threshold parameter with exponential distribution of errors. This is done on a test statistics which is related to a problem of Zvára [Zvara95].
Exact laws for sums of ratios of order statistics from the Pareto distribution
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
We give a stochastic expansion for estimates 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 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
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
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
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 ˜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∗
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 := 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...
Expressions for the probabilities of the bivariate Hermite distribution and related properties
Extremal and additive processes generated by Pareto distributed random vectors
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.
Extremal moment methods and stochastic orders. Application in actuarial science.