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# wbllike

Weibull negative log-likelihood

## Syntax

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

## Description

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

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

where f is the Weibull pdf.

wbllike is a utility function for maximum likelihood estimation.

## Examples

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```