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Non-central bivariate beta distribution

# Non-central bivariate beta distribution,10.1007/s00362-009-0215-y,Statistical Papers,Arjun K. Gupta,Johanna Marcela Orozco-Castañeda,Daya K. Nagar

Non-central bivariate beta distribution
Let U, V and W be independent random variables, U and V having a gamma distribution with respective shape parameters a and b, and W having a non-central gamma distribution with shape and non-centrality parameters c and δ, respectively. Define X = U/(U + W) and Y = V/(V + W). Clearly, X and Y are correlated each having a non-central beta type 1 distribution, $${X \sim {\rm NCB1} (a,c;\delta)}$$ and $${Y \sim {\rm NCB1} (b,c;\delta)}$$ . In this article we derive the joint probability density function of X and Y and study its properties.
Journal: Statistical Papers - STAT PAP , vol. 52, no. 1, pp. 139-152, 2011
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