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A saddlepoint approximation to the distribution of the sum of independent non-identically beta random variables

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  • Saralees Nadarajah
  • Xiao Jiang
  • Jeffrey Chu

Abstract

type="main" xml:id="stan12051-abs-0001"> The exact distribution of the sum of more than two independent beta random variables has not been known. Even in terms of approximations, only the normal approximation is known for the sum. Motivated by Murakami [Statistica Neerlandica, 2014, doi:10.1111/stan.12032], we derive here a saddlepoint approximation for the distribution of sum. An extensive simulation study shows that it always performs better than the normal approximation.

Suggested Citation

  • Saralees Nadarajah & Xiao Jiang & Jeffrey Chu, 2015. "A saddlepoint approximation to the distribution of the sum of independent non-identically beta random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 102-114, May.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:2:p:102-114
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    References listed on IDEAS

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    1. Hidetoshi Murakami, 2014. "A saddlepoint approximation to the distribution of the sum of independent non-identically uniform random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 267-275, November.
    2. Sculli, D & Wong, KL, 1985. "The maximum and sum of two beta variables and the analysis of PERT networks," Omega, Elsevier, vol. 13(3), pages 233-240.
    3. Klein, Robert, 2000. "Scheduling of resource constrained projects," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 1592, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    1. N. N. Midhu & Isha Dewan & K. K. Sudheesh & E. P. Sreedevi, 2024. "On approximation and estimation of distribution function of sum of independent random variables," Statistical Papers, Springer, vol. 65(3), pages 1437-1467, May.

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