Exponential Distribution

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Fathom Reference > Fathom Operators, Functions, and Units > Distribution Functions > Exponential Distribution

For the default values of scale and min (see below), the density function for an exponential distribution is _img128. This means that random values that come from such an exponential distribution are concentrated in the smaller values.

The exponential functions described below take two optional parameters, scale, which defaults to 1, and min, which defaults to 0. The standard deviation of exponentially distributed numbers equals the scale, and the mean equals the sum of the minimum and the scale. We let E represent a random variable having an exponential distribution.

 

A plot of both an exponential density and its cumulative probability.

 

exponentialCumulative (x,

scale, min)

This function computes the cumulative probability, Pr(X ≤ x), where X = min + scale × E.

exponentialDensity (x,

scale, min)

The exponential probability density function is given by

_img129

exponentialQuantile (c,

scale, min)

The exponential quantile function computes the value x, such that Pr(X ≤ x) = c. It is the inverse of exponentialCumulative.