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Pareto Random Variables for Hydrological Modeling

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  • Saralees Nadarajah
  • M. Ali

Abstract

Motivated by hydrological problems, the exact distributions of the sum X + Y, the product X Y and the ratio X/(X + Y) are derived when X and Y are independent Pareto random variables. A detailed application of the results is provided to extreme rainfall data from Florida. Copyright Springer Science+Business Media B.V. 2008

Suggested Citation

  • Saralees Nadarajah & M. Ali, 2008. "Pareto Random Variables for Hydrological Modeling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(10), pages 1381-1393, October.
    • Handle: RePEc:spr:waterr:v:22:y:2008:i:10:p:1381-1393
    DOI: 10.1007/s11269-007-9231-7
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    References listed on IDEAS

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    1. Isameldin Atiem & Nilgün Harmancio˘lu, 2006. "Assessment of Regional Floods Using L-Moments Approach: The Case of The River Nile," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 20(5), pages 723-747, October.
    2. R. W. Farebrother, 1984. "The Distribution of a Positive Linear Combination of X2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(3), pages 332-339, November.
    3. Rakesh Kumar & C. Chatterjee & Sanjay Kumar & A. Lohani & R. Singh, 2003. "Development of Regional Flood Frequency Relationships Using L-moments for Middle Ganga Plains Subzone 1(f) of India," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 17(4), pages 243-257, August.
    4. Tang, Jen & Gupta, A. K., 1984. "On the distribution of the product of independent beta random variables," Statistics & Probability Letters, Elsevier, vol. 2(3), pages 165-168, May.
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    Cited by:

    1. Sang Ug Kim & Cheol-Eung Lee, 2021. "Incorporation of Cost-Benefit Analysis Considering Epistemic Uncertainty for Calculating the Optimal Design Flood," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(2), pages 757-774, January.
    2. Wangxue Chen & Rui Yang & Dongsen Yao & Chunxian Long, 2021. "Pareto parameters estimation using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 62(3), pages 1195-1211, June.
    3. Ribeiro, H.V. & Mendes, R.S. & Lenzi, E.K. & Belancon, M.P. & Malacarne, L.C., 2011. "On the dynamics of bubbles in boiling water," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 178-183.
    4. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, February.
    5. Ferreira, Helena & Ferreira, Marta, 2015. "Extremes of scale mixtures of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 82-99.
    6. Ali İ. Genç, 2021. "Products, Sums and Quotients of Upper Truncated Pareto Random Variables with an Application in Hydrology," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(1), pages 369-383, January.
    7. Walid Abu-Dayyeh & Aissa Assrhani & Kamarulzaman Ibrahim, 2013. "Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling," Statistical Papers, Springer, vol. 54(1), pages 207-225, February.

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