# ExpDev

Calculates deviates from the standard Exponential probability density function

## Contents

### Syntax

Result = StdExpDev( NewDimensions)

### Return Value

StdExpDev returns random deviates drawn from the standard exponential probability function with dimensions NewDimensions. Randomisation depends on the method settings of the function SetRandom().

### Parameters

NewDimensions |structure or matrix with integer values giving the dimensions of the result

### Explanation

The exponential probability density function is

${\displaystyle f(x)={\frac {1}{\beta }}\cdot e^{-\left({\frac {x-\alpha }{\beta }}\right)}}$

with mean of α and β variance of β2 and α=0

The cumulative exponential probability density function is

${\displaystyle F(x)=1-e^{-\left({\frac {x-\alpha }{\beta }}\right)}}$

The exponential deviate is the inverse of F(x) : F-1(p) where p is the probability density and 0=p=1

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>Error fetching URL: Could not resolve host: mathoid.testme.wmflabs.org </p>") from server "http://mathoid.testme.wmflabs.org":): x=\apha-\beta \cdot ln(1-p)

The standard exponential probability density function has α=0 and β=1.

To simulate drawings from the generalized exponential normal probability function a simple transformation is sufficient:

${\displaystyle Deviates=\alpha +\beta \cdot StdNormDev(NewDimensions)}$

### Example

A= expdev (4,5)

expdev(4,5)