Analogues of reliability analysis for matrix-variate cases

Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions

“…If the Maxwell-Boltzmann and Rayleigh densities are the stable distributions in a physical system, then the unstable or chaotic neighborhoods are available from ( 9) and ( 10), and all of the situations, the stable situation, the unstable neighborhoods, and the transitional stages can be reached through the pathway parameter α. For γ = 0, the model in ( 9) is very useful in real multivariate reliability analysis; see [12,13]. The model in (10) for γ = 0 corresponds to a multivariate version of Student-t, Cauchy, multivariate F, and related distributions; see [14].…”

“…For p = 1, we have the scalar variable Maxwell-Boltzmann and Rayleigh densities in the complex domain from (44). The corresponding real cases may be seen from [12,13]. Observe that (43) and (44) also hold for δ < 0, but for δ < 0, the support must be redefined in (42).…”

“…Note that the model in (56) can be taken as the complex rectangular matrix-variate Maxwell-Botzmann and Rayleigh densities for γ = 1 and γ = 1 2 , respectively. The corresponding real cases were given by [12,13]. The standard versions of complex rectangular matrix-variate Maxwell-Boltzmann and Rayleigh densities are available from (56) by considering the density of Y = A…”