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Weibull negative log-likelihood

`nlogL = wbllike(params,data)`

[logL,AVAR] = wbllike(params,data)

[...] = wbllike(params,data,censoring)

[...] = wbllike(params,data,censoring,freq)

`nlogL = wbllike(params,data)`

returns the
Weibull log-likelihood. `params(1)`

is the scale
parameter, `A`

, and `params(2)`

is
the shape parameter, `B`

.

`[logL,AVAR] = wbllike(params,data)`

also
returns `AVAR`

, which is the asymptotic variance-covariance
matrix of the parameter estimates if the values in `params`

are
the maximum likelihood estimates. `AVAR`

is the inverse
of Fisher's information matrix. The diagonal elements of `AVAR`

are
the asymptotic variances of their respective parameters.

`[...] = wbllike(params,data,censoring)`

accepts
a Boolean vector, `censoring`

, of the same size as `data`

,
which is 1 for observations that are right-censored and 0 for observations
that are observed exactly.

`[...] = wbllike(params,data,censoring,freq)`

accepts
a frequency vector, `freq`

, of the same size as `data`

. `freq`

typically
contains integer frequencies for the corresponding elements in `data`

,
but can contain any nonnegative values. Pass in `[]`

for `censoring`

to
use its default value.

The Weibull negative log-likelihood for uncensored data is

$$\left(-\mathrm{log}L\right)=-\mathrm{log}{\displaystyle \prod _{i=1}f\left(a,b|{x}_{i}\right)=-{\displaystyle \sum _{i=1}^{n}\mathrm{log}f\left(a,b|{x}_{i}\right)}}$$

where *f* is the Weibull pdf.

`wbllike`

is a utility function for maximum
likelihood estimation.

This example continues the example from `wblfit`

.

r = wblrnd(0.5,0.8,100,1); [logL, AVAR] = wbllike(wblfit(r),r) logL = 47.3349 AVAR = 0.0048 0.0014 0.0014 0.0040

[1] Patel, J. K., C. H. Kapadia, and D. B.
Owen. *Handbook of Statistical Distributions*.
New York: Marcel Dekker, 1976.