# Dab solver - Reciprocal distribution

./dab_solver.py -page:
0 points on this page / 17,354 points earned collectively this month / Disambiguate pages on your watchlist
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]] of the reciprocal distribution is

: $f( x; a,b ) = \frac{ 1 }{ x [ \log_e( b ) - \log_e( a ) ]} \quad \text{ for } a \le x \le b \text{ and } a > 0.$

Here, a and b are the parameters of the distribution, which are the lower and upper bounds of the [[...|support]], and loge is the [[natural log]] function (the [[logarithm]] to base [[e (mathematical constant)|]]). The [[cumulative distribution function]] is

: $F( x ; a,b) = \frac{ \log_e( x ) - \log_e( a ) }{ \log_e( b ) - \log_e( a ) } \quad \text{ for } a \le x \le b.$

== Applications ==

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

== References ==

{{reflist}}

[[Category:Continuous distributions]]
Single scrollbar