Weibull cumulative distribution function
p = wblcdf(x,a,b)
[p,plo,pup] = wblcdf(x,a,b,pcov,alpha)
[p,plo,pup] = wblcdf(___,'upper')
p = wblcdf(x,a,b) returns the cdf of the
Weibull distribution with scale parameter
b, at each value 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
[p,plo,pup] = wblcdf(x,a,b,pcov,alpha) returns
confidence bounds for
p when the input parameters
pcov is the 2-by-2 covariance matrix
of the estimated parameters.
alpha has a default
value of 0.05, and specifies 100(1 -
arrays of the same size as
p containing the lower
and upper confidence bounds.
[p,plo,pup] = wblcdf(___,'upper') returns
the complement of the Weibull cdf for each value in
using an algorithm that more accurately computes the extreme upper
tail probabilities. You can use
'upper' with any
of the previous syntaxes.
wblcdf computes confidence
p using a normal approximation to the
distribution of the estimate
and then transforms those bounds to the scale of the output
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 Weibull cdf is
What is the probability that a value from a Weibull distribution with parameters
0.8 is less than 0.5?
probability = wblcdf(0.5, 0.15, 0.8)
probability = 0.9272
How sensitive is this result to small changes in the parameters?
[A, B] = meshgrid(0.1:0.05:0.2,0.2:0.05:0.3); probability = wblcdf(0.5, A, B)
probability = 0.7484 0.7198 0.6991 0.7758 0.7411 0.7156 0.8022 0.7619 0.7319