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A Class of Distributions in the First Emptiness of a Semi‐Infinite Reservoir
Author(s) -
Khan M. S. H.,
Jain G. C.
Publication year - 1978
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710200305
Subject(s) - mathematics , gamma distribution , exponential function , emptiness , class (philosophy) , distribution (mathematics) , exponential distribution , natural exponential family , exponential family , homogeneous , probability distribution , mathematical analysis , calculus (dental) , statistical physics , statistics , combinatorics , physics , computer science , medicine , philosophy , theology , dentistry , artificial intelligence
This paper considers the probability distribution of the volume of a certain substance (e.g. river discharge, rainfall, deposites of clay, organism, etc.) that flows into a semi‐infinite reservoir before its first emptiness for continuous and homogeneous input process when the substance is released at unit rate per unit of time. A few moments of the distribution have been computed. A generalized gamma, and a generalized exponential distributions as particular cases are also discussed. Some possible applications of the generalized negative exponential distribution have been mentioned. These distributions are in fact the continuous analogues of the discrete LAGRANGE distributions recently considered by JAIN and others.