A Multivariate Gamma-Type Distribution

Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

“…Or rather its logarithm, inasmuch as the cumulants will be used in the series expansion. 25) where cum m denotes the cumulant of order m. Since…”

“…for half-integer positive α, and arbitrary Σ with property (A.1), the multi-dimensional Γ (α, 2Σ) distribution was defined in [25]. Reference [24] draws our attention to the fact that for m 2, if one makes no restraints for the parameters, other than α > 0 and Σ fulfils (A.1), then (A.3) is not necessarily a characteristic function.…”

Multivariate Nakagami- distribution with constant correlation model

“…The classical Khrishnamoorthy and Parthasarathy [4] multivariate gamma distribution has been used in [5] for evaluating performances of selection combiners (SC) over Nakagami-m correlated channels. Nevertheless, the joint probability density function of [4] involves infinite series of Laguerre polynomials.…”

“…Nevertheless, the joint probability density function of [4] involves infinite series of Laguerre polynomials. Several correlation models have been proposed and used in the literature for evaluating performances of diversity systems.…”

Some Probability Inequalities for Multivariate Gamma and Normal Distributions

“…

AbstractThe Gaussian correlation inequality for multivariate zero-mean normal probabilities of symmetrical n-rectangles can be considered as an inequality for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy [5]) with one degree of freedom. Its generalization to all integer degrees of freedom and sufficiently large non-integer "degrees of freedom" was recently proved in [10].

…”