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On the sum of t and Gaussian random variables

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  • Nason, Guy P.

Abstract

This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student's t-distribution on odd degrees of freedom greater than or equal to three. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calculations in the theoretical analysis of projection indices and computation of certain moments.

Suggested Citation

  • Nason, Guy P., 2006. "On the sum of t and Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1280-1286, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1280-1286
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    References listed on IDEAS

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    1. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, December.
    2. Guy P. Nason, 2001. "Robust projection indices," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 551-567.
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    Cited by:

    1. Mohamed Doukali & Xiaojun Song & Abderrahim Taamouti, 2024. "Value‐at‐Risk under Measurement Error," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 690-713, June.
    2. G. Forchini, 2008. "The distribution of the sum of a normal and a t random variable with arbitrary degrees of freedom," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 205-208.
    3. Berg, C. & Vignat, C., 2010. "On the density of the sum of two independent Student t-random vectors," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1043-1055, July.
    4. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman, 2014. "On Predictive Density Estimation for Location Families under Integrated L 2 and L 1 Losses," CIRJE F-Series CIRJE-F-935, CIRJE, Faculty of Economics, University of Tokyo.
    5. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On predictive density estimation for location families under integrated squared error loss," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 57-74.

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