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

In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. 47 (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika 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) = xf(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).