Geodesic
A method constructing density functions: the case of a generalized Rayleigh variable
Applications of Mathematics, Tome 54 (2009) no. 5, pp. 417-431.

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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 $f(x)$.
DOI : 10.1007/s10492-009-0027-3
Classification : 60E05, 60E10, 60K40, 62P30
Keywords: generalized Rayleigh variable (GRV); generalized exponential (GE); generating differential equation (GDE); conservability; probability density function (p.d.f.); pseudo-Weibull variable 
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Vodă, Viorel Gh. A method constructing density functions: the case of a generalized Rayleigh variable. Applications of Mathematics, Tome 54 (2009) no. 5, pp. 417-431. doi : 10.1007/s10492-009-0027-3. http://geodesic.mathdoc.fr/articles/10.1007/s10492-009-0027-3/

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