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Non-central bivariate beta distribution

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403-0221, USA

    Arjun K. Gupta

  2. Departamento de Matemáticas, Universidad de Antioquia, Calle 67, No. 53–108, Medellín, Colombia

    Johanna Marcela Orozco-Castañeda & Daya K. Nagar

Authors
  1. Arjun K. Gupta
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  2. Johanna Marcela Orozco-Castañeda
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  3. Daya K. Nagar
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Correspondence to Daya K. Nagar.

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Gupta, A.K., Orozco-Castañeda, J.M. & Nagar, D.K. Non-central bivariate beta distribution. Stat Papers 52, 139–152 (2011). https://doi.org/10.1007/s00362-009-0215-y

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  • DOI: https://doi.org/10.1007/s00362-009-0215-y

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