Exponential inverse cumulative distribution function
X = expinv(P,mu)
[X,XLO,XUP] = expinv(X,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(X,mu,pcov,alpha) produces
confidence bounds for
X when the input mean parameter
pcov is the variance of the estimated
confidence bounds. The default value of
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
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
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.