Parameters 0 < a < b , a , b ∈ R {\displaystyle 0 Support [ a , b ] {\displaystyle [a,b]} PDF 1 x [ log e ( b ) − log e ( a ) ] {\displaystyle {\frac {1}{x[\log _{e}(b)-\log _{e}(a)]}}} CDF log e ( x ) − log e ( a ) log e ( b ) − log e ( a ) {\displaystyle {\frac {\log _{e}(x)-\log _{e}(a)}{\log _{e}(b)-\log _{e}(a)}}} Mean b − a log e ( b ) − log e ( a ) {\displaystyle {\frac {b-a}{\log _{e}(b)-\log _{e}(a)}}} | ||
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.
Contents
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,
Differential equation
The pdf of the reciprocal distribution is a solution to the following differential equation:
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.