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Generating random variates from a bicompositional Dirichlet distribution. (English) Zbl 1431.62015

Summary: A composition is a vector of positive components summing to a constant. The sample space of a composition is the simplex, and the sample space of two compositions, a bicomposition, is a Cartesian product of two simplices. We present a way of generating random variates from a bicompositional Dirichlet distribution defined on the Cartesian product of two simplices using the rejection method. We derive a general solution for finding a dominating density function and a rejection constant and also compare this solution to using a uniform dominating density function. Finally, some examples of generated bicompositional random variates, with varying number of components, are presented.

MSC:

62-08 Computational methods for problems pertaining to statistics
65C10 Random number generation in numerical analysis
62E15 Exact distribution theory in statistics
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References:

[1] Aitchison J., The Statistical Analysis of Compositional Data (2003) · Zbl 0491.62017
[2] Bergman J., A bicompositional Dirichlet distribution (2009) · Zbl 1431.62015
[3] DOI: 10.1145/290274.290287 · Zbl 0962.65005 · doi:10.1145/290274.290287
[4] DOI: 10.1090/S0025-5718-98-01004-7 · Zbl 0903.65003 · doi:10.1090/S0025-5718-98-01004-7
[5] DOI: 10.2307/2347565 · Zbl 0825.62407 · doi:10.2307/2347565
[6] DOI: 10.1145/203082.203089 · Zbl 0887.65145 · doi:10.1145/203082.203089
[7] Devroye L., Non-uniform Random Variate Generation (1986) · Zbl 0593.65005 · doi:10.1007/978-1-4613-8643-8
[8] DOI: 10.1080/00949650903409999 · Zbl 1221.62082 · doi:10.1080/00949650903409999
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