Exponential inverse cumulative distribution function
X = expinv(P,mu)
[X,XLO,XUP] = expinv(P,mu,pcov,alpha)
X = expinv(P,mu) computes
the inverse of the exponential
cdf with parameters
specified by mean parameter
mu for the corresponding
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
be positive and the values in
P must lie on the
interval [0 1].
[X,XLO,XUP] = expinv(P,mu,pcov,alpha) produces confidence bounds for
X when the input mean parameter
mu is an estimate.
pcov is the variance of the estimated
alpha specifies 100(1 -
bounds. The default value of
alpha is 0.05.
XUP are arrays of the same size as
X 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
the data to get a confidence interval for
mu, and then evaluating
expinv at the lower and upper end points of that interval.
The inverse of the exponential cdf is
The result, x, is the value such that an observation from an exponential distribution with parameter µ will fall in the range [0 x] with probability p.
Let the lifetime of light bulbs be exponentially distributed with µ = 700 hours. What is the median lifetime of a bulb?
expinv(0.50,700) ans = 485.2030
Suppose you buy a box of “700 hour” light bulbs. If 700 hours is the mean life of the bulbs, half of them will burn out in less than 500 hours.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).