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Some Theorems Concerning Characterization of the W EIBULL Distribution
Author(s) -
Janardan K. G.,
Taneja V. S.
Publication year - 1979
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.4710210207
Subject(s) - weibull distribution , characterization (materials science) , mathematics , distribution (mathematics) , functional equation , exponential distribution , exponential function , gamma distribution , probability distribution , statistical physics , combinatorics , discrete mathematics , statistics , mathematical analysis , physics , differential equation , optics
This paper presents a number of characterizations of the W EIBULL distribution. Some of these results are generalizations of the corresponding results for the exponential distribution. Some characterizing properties lead to a functional equation f ( x ) · f ( y ) = f (( x c + y c ) i/ c ) which is analogous to the C AUCHY functional equation. While the first two characterizations assume somewhat less accessible information concerning the probability distribution, the third and fourth require more readily available information regarding the expected values.