Far East Journal of Theoretical Statistics
Volume 18, Issue 2, Pages 131 - 143
(March 2006)
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RELATIONS BETWEEN THE DEGREE OF SYMMETRY OF THE GAMMA DENSITY
AND THE EXPECTATIONS OF SOME FUNCTIONS OF ORDER STATISTICS: A COMPUTATIONAL
STUDY
Wafik Youssef Younan (Egypt) and Maged George Iskander (Egypt)
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Abstract: This article presents relations between the degree of symmetry
of the gamma density and some quotients of expectations of some functions
of order statistics. The main approach depends on two steps. First,
the theoretical derivation of some inequalities as finite series in the gamma
function, is an intermediate step. Second, using the lower and upper boundaries
of these inequalities to formulate a set of quotients
to be computationally tested in behavior. This leads to discover the relations
that represent the main purpose of the article. The results
are presented for some selected values of the shape parameter of
the gamma distribution which is assumed to be a positive integer.
An application is given to illustrate the possibility of applying the suggested
approach in measuring the inequality degree of income distributions. |
Keywords and phrases: inequalities, gamma distribution, order statistics, Gini’s
coefficient. |
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