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Water Resources Management

, Volume 27, Issue 5, pp 1363–1376 | Cite as

Sums, Products and Ratios for Crovelli’s Bivariate Gamma Distribution

  • Ana Paula C. Madeira Silva
  • Jailson de Araujo RodriguesEmail author
  • Lucas Monteiro Chaves
  • Devanil Jaques de Souza
Article
  • 230 Downloads

Abstract

Bivariate gamma distributions have been used successfully on modeling hydrological processes. In this work, supposing that X and Y follow the Crovelli’s bivariate gamma model, we deduce the exact distributions of the functions U = X + Y, P = XY and Q = X/(X + Y), as well as their respective moments. Those functions are important hidrological variables. A MAPLE code to compute the quantiles is provided. An application of the results is provided to rainfall data from Passo Fundo.

Keywords

Crovelli’s bivariate gamma distribution Sums of random variables Products of random variables Ratios of random variables Moments 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ana Paula C. Madeira Silva
    • 1
  • Jailson de Araujo Rodrigues
    • 2
    Email author
  • Lucas Monteiro Chaves
    • 2
  • Devanil Jaques de Souza
    • 2
  1. 1.Federal University of São João Del Rei - Campus Sete LagoasSete LagoasBrazil
  2. 2.Exact Sciences DepartmentFederal University of Lavras UFLALavrasBrazil

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