Result: Moments of a class of discrete q-distributions

Title:
Moments of a class of discrete q-distributions
Authors:
CHARALAMBIDES, Ch. A
Source:
Special issue on lattice path combinatorics and discrete distributions (in memory of I. Vincze)Journal of statistical planning and inference. 135(1):64-76
Publisher Information:
Amsterdam; Lausanne; New York,NY: Elsevier Science, 2005.
Publication Year:
2005
Physical Description:
print, 10 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Processus de markov, Markov processes, Décision statistique, Statistical decision, Decisión estadística, Fonction génératrice, Generating function, Función generatriz, Fonction répartition, Distribution function, Función distribución, Loi conditionnelle, Conditional distribution, Ley condicional, Loi discrète, Discrete distribution, Ley discreta, Loi probabilité, Probability distribution, Ley probabilidad, Modèle stochastique, Stochastic model, Modelo estocástico, Moment statistique, Statistical moment, Momento estadístico, Méthode statistique, Statistical method, Método estadístico, Probabilité conditionnelle, Conditional probability, Probabilidad condicional, Tirage Bernoulli, Bernoulli trial, Prueba Bernoulli, Variable aléatoire, Random variable, Variable aléatoria, Coefficient q factoriel généralisé, Generalized q factorial coefficient, Moment factoriel, Nombre Stirling, Generalized q-factorial coefficients, Primary 60J10, Secondary 05A30 q-factorial moments, q-Stirling numbers
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, University of Athens, 15784 Athens, Greece
ISSN:
0378-3758
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17042295
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17042295
Database:
PASCAL Archive

Further Information

A wide class of q-distributions is defined on the stochastic model of a sequence of Bernoulli trials in which the conditional probability of success at the nth trial, given that k successes occur before that trial, varies geometrically with n and k. Let Xn be the number of successes up to nth trial and Yk be the number of trials until the occurrence of the kth success. The q-factorial moments of the random variables Xn, and Yk are derived. Further, the usual factorial moments of Xn, which are connected with the q-factorial moments through the q-Stirling numbers of the first kind, are deduced. Finally, the ascending factorial moments of Yk, in the particular case in which the success probability does not depend on n, are obtained through the probability generating function.