Reciprocal distribution | Vose Software

# Reciprocal distribution

Format: Reciprocal(min, max)

The Reciprocal distribution is a right-skewed distribution bounded between min and max. If min and max are almost equal the distribution looks like a Triangle(min,mode,max). The greater the ratio max/min the more the distribution takes on a skewed form. Examples of the Reciprocal distribution are given below:

## Uses

The Reciprocal distribution is widely used as an uninformed prior distribution in Bayesian inference for scale parameters

It is also used to describe '1/f noise'. One way to characterise different noise sources is to consider the spectral density, i.e. the mean squared fluctuation at any particular frequency f and how that varies with frequency. A common approach is to model spectral densities that vary as powers of inverse frequency: the power spectra P(f) is proportional to f -b for b ≥0. b = 0 equates to white noise (i.e. no relationship between P(f) and f), b = 2 is called Brownian noise, and b = 1 takes the name '1/f noise' which occurs very often in nature.

The distribution gets its name because the density function f(x) is proportional to 1/x.

## ModelRisk functions added to Microsoft Excel for the Reciprocal distribution

VoseReciprocal generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseReciprocalObject constructs a distribution object for this distribution.

VoseReciprocalProb returns the probability density or cumulative distribution function for this distribution.

VoseReciprocalProb10 returns the log10 of the probability density or cumulative distribution function.

VoseReciprocalFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseReciprocalFitObject constructs a distribution object of this distribution fitted to data.

VoseReciprocalFitP returns the parameters of this distribution fitted to data.