# exppdf

Exponential probability density function

## Description

example

y = exppdf(x) returns the probability density function (pdf) of the standard exponential distribution, evaluated at the values in x.

example

y = exppdf(x,mu) returns the pdf of the exponential distribution with mean mu, evaluated at the values in x.

## Examples

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Compute the density of the observed value 5 in the standard exponential distribution.

y1 = exppdf(5)
y1 = 0.0067

Compute the density of the observed value 5 in the exponential distributions specified by means 1 through 5.

y2 = exppdf(5,1:5)
y2 = 1×5

0.0067    0.0410    0.0630    0.0716    0.0736

Compute the density of the observed values 1 through 5 in the exponential distributions specified by means 1 through 5, respectively.

y3 = exppdf(1:5,1:5)
y3 = 1×5

0.3679    0.1839    0.1226    0.0920    0.0736

## Input Arguments

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Values at which to evaluate the pdf, specified as a nonnegative scalar value or an array of nonnegative scalar values.

• To evaluate the pdf at multiple values, specify x using an array.

• To evaluate the pdfs of multiple distributions, specify mu using an array.

If either or both of the input arguments x and mu are arrays, then the array sizes must be the same. In this case, exppdf expands each scalar input into a constant array of the same size as the array inputs. Each element in y is the pdf value of the distribution specified by the corresponding element in mu, evaluated at the corresponding element in x.

Example: [3 4 7 9]

Data Types: single | double

Mean of the exponential distribution, specified as a positive scalar value or an array of positive scalar values.

• To evaluate the pdf at multiple values, specify x using an array.

• To evaluate the pdfs of multiple distributions, specify mu using an array.

If either or both of the input arguments x and mu are arrays, then the array sizes must be the same. In this case, exppdf expands each scalar input into a constant array of the same size as the array inputs. Each element in y is the pdf value of the distribution specified by the corresponding element in mu, evaluated at the corresponding element in x.

Example: [1 2 3 5]

Data Types: single | double

## Output Arguments

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pdf values evaluated at the values in x, returned as a scalar value or an array of scalar values. y is the same size as x and mu after any necessary scalar expansion. Each element in y is the pdf value of the distribution specified by the corresponding element in mu, evaluated at the corresponding element in x.

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### Exponential pdf

The exponential distribution is a one-parameter family of curves. The parameter μ is the mean.

The pdf of the exponential distribution is

$y=f\left(x|\mu \right)=\frac{1}{\mu }{e}^{\frac{-x}{\mu }}.$

A common alternative parameterization of the exponential distribution is to use λ defined as the mean number of events in an interval as opposed to μ, which is the mean wait time for an event to occur. λ and μ are reciprocals.

## Alternative Functionality

• exppdf is a function specific to the exponential distribution. Statistics and Machine Learning Toolbox™ also offers the generic function pdf, which supports various probability distributions. To use pdf, create an ExponentialDistribution probability distribution object and pass the object as an input argument or specify the probability distribution name and its parameters. Note that the distribution-specific function exppdf is faster than the generic function pdf.

• Use the Probability Distribution Function app to create an interactive plot of the cumulative distribution function (cdf) or probability density function (pdf) for a probability distribution.

## Version History

Introduced before R2006a