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

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  • Hidetoshi Murakami

Abstract

type="main" xml:id="stan12032-abs-0001"> Calculating the probability of the corresponding significance point is important for finite sample sizes. However, it is difficult to evaluate this probability when the sample sizes are moderate to large. Under these circumstances, consideration of a more accurate approximation for the distribution function is extremely important. Herein, we performed a saddlepoint approximation in the upper tails for the distribution of the sum of independent non-identically uniform random variables under finite sample sizes. Saddlepoint approximation results were compared with those for a normal approximation. Additionally, the order of errors of the saddlepoint approximation was derived. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:stanee:v:68:y:2014:i:4:p:267-275
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    File URL: http://hdl.handle.net/10.1111/stan.12032
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    References listed on IDEAS

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    1. Rob Eisinga & Manfred Te Grotenhuis & Ben Pelzer, 2013. "Saddlepoint approximations for the sum of independent non-identically distributed binomial random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(2), pages 190-201, May.
    2. S. Sadooghi-Alvandi & A. Nematollahi & R. Habibi, 2009. "On the distribution of the sum of independent uniform random variables," Statistical Papers, Springer, vol. 50(1), pages 171-175, January.
    3. David Bradley & Ramesh Gupta, 2002. "On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 689-700, September.
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    Cited by:

    1. 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.
    2. James E. Marengo & David L. Farnsworth & Lucas Stefanic, 2017. "A Geometric Derivation of the Irwin-Hall Distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-6, September.

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