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Titre du document / Document title

A concept of generalized order statistics

Auteur(s) / Author(s)

KAMPS U. ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

Aachen univ. technology, inst. statistics, 52056 Aachen, ALLEMAGNE

Résumé / Abstract

A form of the joint distribution of n ordered random variables is presented that enables a unified approach to a variety of models of ordered random variables, e.g. order statistics and record values. Several other models are shown. In particular, sequential order statistics are introduced as a modification of order statistics which is naturally suggested by a statistical application in reliability theory. In the distribution theoretical sense, all of these models of ordered random variables are contained in the proposed concept of generalized order statistics. Numerous related results on distributional and moment properties of ordinary order statistics and record values are found in the literature which are deduced separately. Generalized order statistics, however, provide a suitable approach to explain these similarities and analogies in the two models and to generalize related results. Through integration of known properties the structure of the embedded models becomes clearer. On the other hand, we obtain the validity of these properties and their generalizations for generalized order statistics, and hence for different models of ordered random variables. In the present paper we develop the distribution theory for generalized order statistics. Representations for the one-, two- and higher-dimensional marginal densities and a form of the one-dimensional marginal distribution functions are given as well as recurrence relations for marginal densities and distribution functions. Moreover, we give representations for moments and differences of moments of generalized order statistics, sufficient conditions for the existence of moments, and we show some explicit expressions for the moments of generalized order statistics based on power function, Pareto and Weibull distributions.

Revue / Journal Title

Journal of statistical planning and inference    ISSN  0378-3758   CODEN JSPIDN 

Source / Source

1995, vol. 48, no1, pp. 1-23 (2 p.)

Langue / Language

Anglais

Editeur / Publisher

Elsevier, Kidlington, ROYAUME-UNI  (1977) (Revue)

Mots-clés anglais / English Keywords

Order statistic

;

Distribution function

;

Statistical moment

;

Joint distribution

;

Probability theory

;

Random variable

;

Reliability

;

Statistical model

;

Generalization

;

Record value

;

Mots-clés français / French Keywords

Statistique ordre

;

Fonction répartition

;

Moment statistique

;

Loi conjointe

;

Théorie probabilité

;

Variable aléatoire

;

Fiabilité

;

Modèle statistique

;

Généralisation

;

Statistique ordre séquentielle

;

Variable ordonnée

;

Différence moment

;

Valeur record

;

Mots-clés espagnols / Spanish Keywords

Estadística orden

;

Función distribución

;

Momento estadístico

;

Ley conjunta

;

Teoría probabilidad

;

Variable aléatoria

;

Fiabilidad

;

Modelo estadístico

;

Generalización

;

Localisation / Location

INIST-CNRS, Cote INIST : 17575, 35400005849808.0010

Nº notice refdoc (ud4) : 2929047



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