CODEWITHSUNDEEP
rrandomgamma-distribution
fsbmat
fsbmat

Reputation: 301

Generate random numbers with bivariate gamma distribution in R

How to generate random numbers with bivariate gamma distribution. The density is:

F(X, Y)(x, y) = αp+qxp-1(y-x)q-1e-αy / [Γ(p) Γ(q)], 𝕀0≤ x≤ y

With y>x>0, α>0, p>0 and q>0.

I did not find any package on R that does this and nothing in literature.

Upvotes: 2

Views: 1871

Answers (1)

Glen_b
Glen_b

Reputation: 8252

This is straightforward:

  1. Generate X~ Gamma(p,alpha) (alpha being the rate parameter in your formulation)

  2. Generate W~ Gamma(q,alpha), independent of X

  3. Calculate Y=X+W

  4. (X,Y) have the required bivariate distribution.

in R (assuming p,q,alpha and n are already defined):

x <- rgamma(n,p,alpha)
y <- x + rgamma(n,q,alpha)

generates n values from the bivariate distribution with parameters p,q,alpha

Upvotes: 1

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