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Scenario generation with distribution functions and correlations

Michal Kaut, Arnt-Gunnar Lium (2014)

Kybernetika

In this paper, we present a method for generating scenarios for two-stage stochastic programs, using multivariate distributions specified by their marginal distributions and the correlation matrix. The margins are described by their cumulative distribution functions and we allow each margin to be of different type. We demonstrate the method on a model from stochastic service network design and show that it improves the stability of the scenario-generation process, compared to both sampling and a...

Sharp bounds for expectations of spacings from decreasing density and failure rate families

Katarzyna Danielak, Tomasz Rychlik (2004)

Applicationes Mathematicae

We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.

Simple large sample estimators of scale and location parameters based on blocks of order statistics.

Peter Kubat (1982)

Trabajos de Estadística e Investigación Operativa

In this paper quite efficient large sample estimation procedures are derived for jointly estimating the parameters of the location-scale family of distributions. These estimators are linear combinations of the means of suitably chosen blocks of order statistics. For specific distributions, such as the extreme-value, normal, and logistic, little is to be gained by using more than three blocks. For these distributions we can obtain joint relative asymptotic efficiencies of 97-98% using the means of...

Simple random walk and rank order statistics

Igor Očka (1977)

Aplikace matematiky

The distributions of rank order statistics are studied for the case of arbitrary sample sizes in the two sample problem. The method applied is a generalization of Dwass's method from his paper in Ann. Math. Statist. 38 (1967), based on the analogy of rank order statistics and functions on a simple random walk.

Some limit behavior for linear combinations of order statistics

Yu Miao, Mengyao Ma (2021)

Kybernetika

In the present paper, we establish the moderate and large deviations for the linear combinations of uniform order statistics. As applications, the moderate and large deviations for the k -th order statistics from uniform distribution, Gini mean difference statistics and the k -th order statistics from general continuous distribution are obtained.

Sparsity in penalized empirical risk minimization

Vladimir Koltchinskii (2009)

Annales de l'I.H.P. Probabilités et statistiques

Let (X, Y) be a random couple in S×T with unknown distribution P. Let (X1, Y1), …, (Xn, Yn) be i.i.d. copies of (X, Y), Pn being their empirical distribution. Let h1, …, hN:S↦[−1, 1] be a dictionary consisting of N functions. For λ∈ℝN, denote fλ:=∑j=1Nλjhj. Let ℓ:T×ℝ↦ℝ be a given loss function, which is convex with respect to the second variable. Denote (ℓ•f)(x, y):=ℓ(y; f(x)). We study the following penalized empirical risk minimization problem λ ^ ε : = argmin λ ∈ ℝ N P n ( ℓ • f λ ) + ε ∥ λ ∥ ℓ p p , which is an empirical version of the problem λ ε : = argmin λ ∈ ℝ N P ( ℓ • f λ ) + ε ∥ λ ∥ ℓ p p (hereɛ≥0...

Stress-strength based on m -generalized order statistics and concomitant for dependent families

Filippo Domma, Abbas Eftekharian, Mostafa Razmkhah (2019)

Applications of Mathematics

The stress-strength model is proposed based on the m -generalized order statistics and the corresponding concomitant. For the dependency between m -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional reversed...

Subset selection of the largest location parameter based on L -estimates

Jaroslav Hustý (1984)

Aplikace matematiky

The problem of selecting a subset of polulations containing the population with the largest location parameter is considered. As a generalization of selection rules based on sample means and on sample medians, a rule based on L -estimates of location is proposed. This rule is strongly monotone and minimax, the risk being the expected subset size, provided the underlying density has monotone likelihood ratio. The problem of fulfilling the P * -condition is solved explicitly only asymptotically, under...

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