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Generation of discrete random variables in scalable frameworks

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  • Aletti, Giacomo

Abstract

In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add parallelized randomness, and we leave the final simulation of the random variable to a single associative operation. We characterize the set of algorithms that work in this way, and those algorithms that may have an additive or multiplicative local noise. As a consequence, we could define a natural way to solve some popular simulation problems.

Suggested Citation

  • Aletti, Giacomo, 2018. "Generation of discrete random variables in scalable frameworks," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 99-106.
    • Handle: RePEc:eee:stapro:v:132:y:2018:i:c:p:99-106
    DOI: 10.1016/j.spl.2017.09.004
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    References listed on IDEAS

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    1. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2004. "Fast Generation of Discrete Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i03).
    2. Devroye, Luc, 2012. "A note on generating random variables with log-concave densities," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1035-1039.
    3. David J. Hand & Keming Yu, 2001. "Idiot's Bayes—Not So Stupid After All?," International Statistical Review, International Statistical Institute, vol. 69(3), pages 385-398, December.
    4. Shmerling, Efraim, 2013. "A range reduction method for generating discrete random variables," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1094-1099.
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