On an inequality and the related characterization of the gamma distribution
Applications of Mathematics (1993)
- Volume: 38, Issue: 1, page 11-18
- ISSN: 0862-7940
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topKoicheva, Maia. "On an inequality and the related characterization of the gamma distribution." Applications of Mathematics 38.1 (1993): 11-18. <http://eudml.org/doc/15732>.
@article{Koicheva1993,
abstract = {In this paper we derive conditions upon the nonnegative random variable under which the inequality $Dg(\xi )\le cE\left[g^\{\prime \}\left(\xi \right)\right]^2\xi $ holds for a fixed nonnegative constant $c$ and for any absolutely continuous function $g$. Taking into account the characterization of a Gamma distribution we consider the functional $U_\xi = \sup _g \frac\{Dg\left(\xi \right)\}\{E\left[g^\{\prime \}\left(\xi \right)\right]^2\xi \}$ and establishing some of its properties we show that $U_\xi \ge 1$ and that $U_\xi =1$ iff the random variable $\xi $ has a Gamma distribution.},
author = {Koicheva, Maia},
journal = {Applications of Mathematics},
keywords = {characterizations; Gamma distribution; characterization of a gamma distribution},
language = {eng},
number = {1},
pages = {11-18},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On an inequality and the related characterization of the gamma distribution},
url = {http://eudml.org/doc/15732},
volume = {38},
year = {1993},
}
TY - JOUR
AU - Koicheva, Maia
TI - On an inequality and the related characterization of the gamma distribution
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 1
SP - 11
EP - 18
AB - In this paper we derive conditions upon the nonnegative random variable under which the inequality $Dg(\xi )\le cE\left[g^{\prime }\left(\xi \right)\right]^2\xi $ holds for a fixed nonnegative constant $c$ and for any absolutely continuous function $g$. Taking into account the characterization of a Gamma distribution we consider the functional $U_\xi = \sup _g \frac{Dg\left(\xi \right)}{E\left[g^{\prime }\left(\xi \right)\right]^2\xi }$ and establishing some of its properties we show that $U_\xi \ge 1$ and that $U_\xi =1$ iff the random variable $\xi $ has a Gamma distribution.
LA - eng
KW - characterizations; Gamma distribution; characterization of a gamma distribution
UR - http://eudml.org/doc/15732
ER -
References
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