Weibull inverse cumulative distribution function
X = wblinv(P,A,B)
[X,XLO,XUP] = wblinv(P,A,B,PCOV,alpha)
X = wblinv(P,A,B) returns the inverse cumulative
distribution function (cdf) for a Weibull distribution with scale
A and shape parameter
evaluated at the values in
B can be vectors, matrices, or multidimensional
arrays that all have the same size. A scalar input is expanded to
a constant array of the same size as the other inputs. The default
B are both
[X,XLO,XUP] = wblinv(P,A,B,PCOV,alpha) returns
confidence bounds for
X when the input parameters
PCOV is a 2-by-2 matrix containing the
covariance matrix of the estimated parameters.
a default value of 0.05, and specifies 100(1 -
alpha)% confidence bounds.
arrays of the same size as
X containing the lower
and upper confidence bounds.
wblinv computes confidence bounds
X using a normal approximation to the distribution
of the estimate
where q is the
from a Weibull distribution with scale and shape parameters both equal
to 1. The computed bounds give approximately the desired confidence
level when you estimate
PCOV from large samples, but in smaller samples
other methods of computing the confidence bounds might be more accurate.
The inverse of the Weibull cdf is
The lifetimes (in hours) of a batch of light bulbs has a Weibull
distribution with parameters
200 and b =
Find the median lifetime of the bulbs:
life = wblinv(0.5, 200, 6) life = 188.1486
Generate 100 random values from this distribution, and estimate the 90th percentile (with confidence bounds) from the random sample
x = wblrnd(200,6,100,1); p = wblfit(x) [nlogl,pcov] = wbllike(p,x) [q90,q90lo,q90up] = wblinv(0.9,p(1),p(2),pcov) p = 204.8918 6.3920 nlogl = 496.8915 pcov = 11.3392 0.5233 0.5233 0.2573 q90 = 233.4489 q90lo = 226.0092 q90up = 241.1335
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