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 24 Next

Displaying 461 – 480 of 654

Showing per page

On the optimality of the empirical risk minimization procedure for the convex aggregation problem

Guillaume Lecué, Shahar Mendelson (2013)

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

We study the performance of empirical risk minimization (ERM), with respect to the quadratic risk, in the context of convex aggregation, in which one wants to construct a procedure whose risk is as close as possible to the best function in the convex hull of an arbitrary finite class F . We show that ERM performed in the convex hull of F is an optimal aggregation procedure for the convex aggregation problem. We also show that if this procedure is used for the problem of model selection aggregation,...

On the optimality of the max-depth and max-rank classifiers for spherical data

Ondřej Vencálek, Houyem Demni, Amor Messaoud, Giovanni C. Porzio (2020)

Applications of Mathematics

The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers for directional data are optimal. We show that such classifiers are equivalent to the Bayes...

On the order equivalence relation of binary association measures

Mariusz Paradowski (2015)

International Journal of Applied Mathematics and Computer Science

Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association measures...

On the outstanding elements and record values in the exponential and gamma populations.

G. S. Lingappaiah (1981)

Trabajos de Estadística e Investigación Operativa

Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution...

On the probability of reaching a barrier in an Erlang(2) risk process.

M. Mercè Claramunt, M. Teresa Mármol, Ramón Lacayo (2005)

SORT

In this paper the process of aggregated claims in a non-life insurance portfolio as defined in the classical model of risk theory is modified. The Compound Poisson process is replaced with a more general renewal risk process with interocurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, χ(u,b). Our main contribution is the generalization obtained in the computation of χ(u,b) for the case of interocurrence...

On the problem of the means of weighted normal populations.

Mikhail S. Nikulin, Vassiliy G. Voinov (1995)

Qüestiió

An analytical problem, which arises in the statistical problem of comparing the means of two normal distributions, the variances of which -as well as their ratio- are unknown, is well known in the mathematical statistics as the Behrens-Fisher problem. One generalization of the Behrens-Fisher problem and different aspect concerning the estimation of the common mean of several independent normal distributions with different variances are considered and one solution is proposed.

On the product of triangular random variables

Mridula Garg, Sangeeta Choudhary, Saralees Nadarajah (2009)

Applicationes Mathematicae

We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.

On the properties of the Generalized Normal Distribution

Thomas L. Toulias, Christos P. Kitsos (2014)

Discussiones Mathematicae Probability and Statistics

The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.

On the Rao-Blackwell Theorem for fuzzy random variables

María Asunción Lubiano, María Angeles Gil, Miguel López-Díaz (1999)

Kybernetika

In a previous paper, conditions have been given to compute iterated expectations of fuzzy random variables, irrespectively of the order of integration. In another previous paper, a generalized real-valued measure to quantify the absolute variation of a fuzzy random variable with respect to its expected value have been introduced and analyzed. In the present paper we combine the conditions and generalized measure above to state an extension of the basic Rao–Blackwell Theorem. An application of this...

On the ratio of gamma and Rayleigh random variables

Saralees Nadarajah (2007)

Applicationes Mathematicae

The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.

Currently displaying 461 – 480 of 654