Alex Herbert created STATISTICS-58:
--------------------------------------
Summary: Investigate the discrete distribution inverse probability
default implementation
Key: STATISTICS-58
URL: https://issues.apache.org/jira/browse/STATISTICS-58
Project: Commons Statistics
Issue Type: Task
Components: distribution
Affects Versions: 1.0
Reporter: Alex Herbert
The default inverse probability implementation for the discrete distributions
uses a simple bisection search within an initial bracket. Bracketing is based
on the mean and variance of the distribution and the input p-value.
The worst case scenario is a bracket between Integer min and max value (range
2^32 -1). A bisection search would require 32 iterations to find the value x
for input probability p.
{noformat}
// Range [a, b]
max = log2(b - a){noformat}
The following distributions are currently in the library:
||Distribution||a||b||Notes||
|Binomial(n, p)|0|n| |
|Geometric(p)|0|infinity|Inverted using a formula|
|Hypergeometric(N, K, n)|max(0, n+K-N) |min(n, k)| |
|Pascal(n, p)|0|infinity|Negative binomial distribution|
|Poisson(mu)|0|infinity| |
|Uniform(a, b)|a|b|Inverted using a formula|
|Zipf(N, s)|1|N| |
For several of the distributions the range is limited by the parameters.
Notable exceptions are the Pascal and Poisson distribution. An investigation
should be made to determine the number of iterations required for inversion and
whether this can be improved.
--
This message was sent by Atlassian Jira
(v8.20.10#820010)
