wblcdf
Weibull cumulative distribution function
Syntax
p = wblcdf(x,a,b)
[p,plo,pup] = wblcdf(x,a,b,pcov,alpha)
[p,plo,pup] = wblcdf(___,'upper')
Description
p = wblcdf(x,a,b)
returns the cdf of the
Weibull distribution with scale parameter a
and
shape parameter b
, at each value in x
. x
, a
,
and 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
values for a
and b
are both 1
.
The parameters a
and b
must
be positive.
[p,plo,pup] = wblcdf(x,a,b,pcov,alpha)
returns
confidence bounds for p
when the input parameters a
and b
are
estimates. pcov
is the 2-by-2 covariance matrix
of the estimated parameters. alpha
has a default
value of 0.05, and specifies 100(1 - alpha
)%
confidence bounds. plo
and pup
are
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 x
,
using an algorithm that more accurately computes the extreme upper
tail probabilities. You can use 'upper'
with any
of the previous syntaxes.
The function wblcdf
computes confidence
bounds for p
using a normal approximation to the
distribution of the estimate
and then transforms those bounds to the scale of the output p
.
The computed bounds give approximately the desired confidence level
when you estimate mu
, sigma
,
and pcov
from large samples, but in smaller samples
other methods of computing the confidence bounds might be more accurate.
The Weibull cdf is