Generalized length biased distributions

Lingappaiah, Giri S.. "Generalized length biased distributions." Aplikace matematiky 33.5 (1988): 354-361. <http://eudml.org/doc/15549>.

@article{Lingappaiah1988,
abstract = {Generalized length biased distribution is defined as $h(x)=\phi _r (x)f(x), x>0$, where $f(x)$ is a probability density function, $\phi _r (x)$ is a polynomial of degree $r$, that is, $\phi _r (x)=a_1(x/\mu ^\{\prime \}_1)+ \ldots + a_r(x^r/\mu ^\{\prime \}_r)$, with $a_i>0, i=1,\ldots ,r, a_1+\ldots + a_r=1, \mu ^\{\prime \}_i=E(x^i)$ for $f(x), i=1,2 \ldots , r$. If $r=1$, we have the simple length biased distribution of Gupta and Keating [1]. First, characterizations of exponential, uniform and beta distributions are given in terms of simple length biased distributions. Next, for the case of generalized distribution, the distribution of the sum of $n$ independent variables is put in the closed form when $f(x)$ is exponential. Finally, Bayesian estimates of $a_1, \ldots , a_r$ are obtained for the generalized distribution for general $f(x), x>1$.},
author = {Lingappaiah, Giri S.},
journal = {Aplikace matematiky},
keywords = {characterizations; exponential; uniform; beta distributions; length biased distributions; Bayesian estimates; characterizations; exponential; uniform; beta distributions; length biased distributions; Bayesian estimates},
language = {eng},
number = {5},
pages = {354-361},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized length biased distributions},
url = {http://eudml.org/doc/15549},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Lingappaiah, Giri S.
TI - Generalized length biased distributions
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 5
SP - 354
EP - 361
AB - Generalized length biased distribution is defined as $h(x)=\phi _r (x)f(x), x>0$, where $f(x)$ is a probability density function, $\phi _r (x)$ is a polynomial of degree $r$, that is, $\phi _r (x)=a_1(x/\mu ^{\prime }_1)+ \ldots + a_r(x^r/\mu ^{\prime }_r)$, with $a_i>0, i=1,\ldots ,r, a_1+\ldots + a_r=1, \mu ^{\prime }_i=E(x^i)$ for $f(x), i=1,2 \ldots , r$. If $r=1$, we have the simple length biased distribution of Gupta and Keating [1]. First, characterizations of exponential, uniform and beta distributions are given in terms of simple length biased distributions. Next, for the case of generalized distribution, the distribution of the sum of $n$ independent variables is put in the closed form when $f(x)$ is exponential. Finally, Bayesian estimates of $a_1, \ldots , a_r$ are obtained for the generalized distribution for general $f(x), x>1$.
LA - eng
KW - characterizations; exponential; uniform; beta distributions; length biased distributions; Bayesian estimates; characterizations; exponential; uniform; beta distributions; length biased distributions; Bayesian estimates
UR - http://eudml.org/doc/15549
ER -