# gamlike

Gamma negative log-likelihood

## Syntax

```nlogL = gamlike(params,data) [nlogL,AVAR] = gamlike(params,data) ```

## Description

`nlogL = gamlike(params,data)` returns the negative of the gamma log-likelihood of the parameters, `params`, given `data`. `params(1)=A`, shape parameters, and `params(2)=B`, scale parameters. The parameters in `params` must all be positive

`[nlogL,AVAR] = gamlike(params,data)` also returns `AVAR`, which is the asymptotic variance-covariance matrix of the parameter estimates when 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.

`[...] = gamlike(params,data,censoring)` accepts a Boolean vector of the same size as `data` that is 1 for observations that are right-censored and 0 for observations that are observed exactly.

`[...] = gamfit(params,data,censoring,freq)` accepts a frequency vector of the same size as `data`. `freq` typically contains integer frequencies for the corresponding elements in `data`, but may contain any non-negative values.

`gamlike` is a utility function for maximum likelihood estimation of the gamma distribution. Since `gamlike` returns the negative gamma log-likelihood function, minimizing `gamlike` using `fminsearch` is the same as maximizing the likelihood.

## Examples

Compute the negative log-likelihood of parameter estimates computed by the `gamfit` function:

```a = 2; b = 3; r = gamrnd(a,b,100,1); [nlogL,AVAR] = gamlike(gamfit(r),r) nlogL = 267.5648 AVAR = 0.0788 -0.1104 -0.1104 0.1955```

## Version History

Introduced before R2006a