Hello expensive customer to our community We will proffer you an answer to this query integration – fractional moments of multivariate regular distributions ,and the respond will breathe typical by documented info sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query.

integration – fractional moments of multivariate regular distributions

Mathematica offers some outcomes for the bivariate regular distribution with correlation $rho$ and benchmark marginals. If $a$ and $b$ are constructive integers then

commence{align}

textual content{for queer }a+b, E[x^a y^b]
&=0

textual content{for queer }atext{ and }b, E[x^a y^b]
&=

sqrt{frac{2^{a+1}}pi}

Gamma!left(1+frac a2right)

f(a,b,rho)

textual content{for plane }atext{ and }b, E[x^a y^b]
&=

sqrt{frac{2^{a}}pi}

Gamma!left(1+frac a2right)

f(a,b,rho)

aim{align}

the place

commence{align}

f(a,1,rho)&=rho

f(a,3,rho)&=3rho+(a-1)rho^3

f(a,5,rho)&=15rho+10(a-1)rho^3+(a-1)(a-3)rho^5

f(a,2,rho)&=1+arho^2

f(a,4,rho)&=3+6arho^2+a(a-2)rho^4

f(a,6,rho)&=15+45arho^2+15a(a-2)rho^4 + a(a-2)(a-4)rho^6

aim{align}

For queer $a$ and $b$ the coefficients emerge to breathe Ward numbers, and for plane $a$ and $b$ they emerge to breathe the exponential Riordan array.

we are going to proffer you the answer to integration – fractional moments of multivariate regular distributions query through our community which brings all of the solutions from a number of dependable sources.

## Add comment