# Efficient Sampling Methods for Discrete Distributions

Efficient Sampling Methods for Discrete Distributions We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities \$\$p_1, \dots , p_n\$\$ p 1 , ⋯ , p n . First, we consider the problem of sampling from the distribution where the i-th event has probability proportional to \$\$p_i\$\$ p i . Second, we study the problem of sampling a subset which includes the i-th event independently with probability \$\$p_i\$\$ p i . For both problems we present on two different classes of inputs—sorted and general probabilities—efficient data structures consisting of a preprocessing and a query algorithm. Varying the allotted preprocessing time yields a trade-off between preprocessing and query time, which we prove to be asymptotically optimal everywhere. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

# Efficient Sampling Methods for Discrete Distributions

, Volume 79 (2) – Aug 29, 2016
25 pages

/lp/springer_journal/efficient-sampling-methods-for-discrete-distributions-nPDf9zIYRS
Publisher
Springer US
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-016-0205-0
Publisher site
See Article on Publisher Site

### Abstract

We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities \$\$p_1, \dots , p_n\$\$ p 1 , ⋯ , p n . First, we consider the problem of sampling from the distribution where the i-th event has probability proportional to \$\$p_i\$\$ p i . Second, we study the problem of sampling a subset which includes the i-th event independently with probability \$\$p_i\$\$ p i . For both problems we present on two different classes of inputs—sorted and general probabilities—efficient data structures consisting of a preprocessing and a query algorithm. Varying the allotted preprocessing time yields a trade-off between preprocessing and query time, which we prove to be asymptotically optimal everywhere.

### Journal

AlgorithmicaSpringer Journals

Published: Aug 29, 2016

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