A method constructing density functions: the case of a generalized Rayleigh variable

summary:In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. {\it 47} (1976), pp.\,395--412. The construction makes use of the so-called ``conservability approach'' (see Kybernetika {\it 25} (1989), pp.\,209--215) namely, if $X$ is a positive continuous random variable with a finite mean-value $E(X)$, then a new density is set to be $f_1(x) = x f(x)/E(X)$, where $f(x)$ is the probability density function of $X$. The new generalized Rayleigh variable is obtained using a generalized form of the exponential distribution introduced by Isaic-Maniu and the present author as $f(x)$