Exactly Computing the Tail of the Poisson-Binomial Distribution

被引：2

作者：

Peres, Noah ^{[1
]}

Lee, Andrew Ray ^{[1
]}

Keich, Uri ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | 2021年 / 47卷 / 04期

关键词：

Poisson-binomial; exact method; FFT; exponential shift; COMPUTATION;

D O I：

10.1145/3460774

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.

引用

页数：19

共 50 条

[21] FITTING THE POISSON BINOMIAL DISTRIBUTION
SHUMWAY, R
GURLAND, J
BIOMETRICS, 1960, 16 (04) : 522 - 533
[22] Poisson Mixture of Poisson and Negative Binomial Distribution
Roy, D. C.
Sinha, S. K.
Journal of the Bangladesh Academy of Sciences,
[23] On the Poisson approximation of the binomial distribution
Ruzankin, PS
SIBERIAN MATHEMATICAL JOURNAL, 2001, 42 (02) : 353 - 363
[24] Testing deviation for a set of serial dilution most probable numbers from a Poisson-binomial model
U.S. Food and Drug Administration, 5100 Paint Branch Pkwy, College Park, MD 20740, United States
J AOAC Int, 2006, 1 (166-171):
[25] Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion
Roos, B
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2000, 45 (02) : 258 - 272
[26] Testing deviation for a set of serial dilution most probable numbers from a Poisson-binomial model
Blodgett, RJ
JOURNAL OF AOAC INTERNATIONAL, 2006, 89 (01) : 166 - 171
[27] A MOMENT INEQUALITY WITH APPLICATION TO CONVERGENCE RATE ESTIMATES IN THE GLOBAL CLT FOR POISSON-BINOMIAL RANDOM SUMS
Shevtsova, I. G.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2018, 62 (02) : 278 - 294
[28] THE POISSON APPROXIMATION TO THE BINOMIAL-DISTRIBUTION
SHEU, SS
AMERICAN STATISTICIAN, 1984, 38 (03): : 206 - 207
[29] On the convergence of Markov binomial to Poisson distribution
Cekanavicius, V
STATISTICS & PROBABILITY LETTERS, 2002, 58 (01) : 83 - 91
[30] Efficient computation for the Poisson binomial distribution
Barrett, Bruce E.
Gray, J. Brian
COMPUTATIONAL STATISTICS, 2014, 29 (06) : 1469 - 1479

← 1 2 3 4 5 →