Exponential cumulative distribution function

`p = expcdf(x,mu)`

[p,plo,pup] = expcdf(x,mu,pcov,alpha)

[p,plo,pup] = expcdf(___,'upper')

`p = expcdf(x,mu)`

computes
the exponential cdf at each of the values in `x`

using
the corresponding mean parameter `mu`

. `x`

and `mu`

can
be vectors, matrices, or multidimensional arrays that all have the
same size. A scalar input is expanded to a constant array with the
same dimensions as the other input. The parameters in `mu`

must
be positive.

`[p,plo,pup] = expcdf(x,mu,pcov,alpha)`

produces confidence bounds for
`p`

when the input mean parameter `mu`

is an
estimate. `pcov`

is the variance of the estimated
`mu`

. `alpha`

specifies
100(1 - `alpha`

)% confidence bounds. The default value of
`alpha`

is 0.05. `plo`

and `pup`

are arrays of the same size as `p`

containing the lower and upper
confidence bounds. The bounds are based on a normal approximation for the distribution
of the log of the estimate of `mu`

. If you estimate
`mu`

from a set of data, you can get a more accurate set of bounds
by applying `expfit`

to the data to get a confidence interval for
`mu`

, and then evaluating `expinv`

at the lower
and upper endpoints of that interval.

`[p,plo,pup] = expcdf(___,'upper')`

returns
the complement of the exponential cdf at each value in `x`

,
using an algorithm that more accurately computes the extreme upper
tail probabilities. You can use the `'upper'`

argument
with any of the prior syntaxes.

The exponential cdf is

$$p=F(x|u)={\displaystyle \underset{0}{\overset{x}{\int}}\frac{1}{\mu}}{e}^{\frac{-t}{\mu}}dt=1-{e}^{\frac{-x}{\mu}}$$

The result, *p*, is the probability that a
single observation from an exponential distribution will fall in the
interval [0 *x*].