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Reciprocal distribution

From Wikipedia, the free encyclopedia

Reciprocal
Parameters
Support
PDF
CDF
Mean

In probability and statistics, the reciprocal distribution is a continuous probability distribution. It is characterised by its probability density function, within the support of the distribution, being proportional to the reciprocal of the variable.

The reciprocal distribution is an example of an inverse distribution, and the reciprocal (inverse) of a random variable with a reciprocal distribution itself has a reciprocal distribution.

Definition

The probability density function (pdf) of the reciprocal distribution is

Here, and are the parameters of the distribution, which are the lower and upper bounds of the support, and is the natural log function (the logarithm to base e). The cumulative distribution function is

Applications

The reciprocal distribution is of considerable importance in numerical analysis as a computer’s arithmetic operations transform mantissas with initial arbitrary distributions to the reciprocal distribution as a limiting distribution.[1]

References

  1. ^ Hamming R. W. (1970) "On the distribution of numbers", The Bell System Technical Journal 49(8) 1609–1625
This page was last edited on 16 January 2018, at 10:31
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