Extreme value negative log-likelihood

`nlogL = evlike(params,data)`

[nlogL,AVAR] = evlike(params,data)

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

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

`nlogL = evlike(params,data)`

returns the
negative of the log-likelihood for the type 1 extreme value distribution. `params(1)`

is
the tail location parameter, `mu`

, and `params(2)`

is
the scale parameter, `sigma`

. `nlogL`

is
a scalar.

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

returns
the inverse of Fisher's information matrix, `AVAR`

.
If the input parameter values in `params`

are the
maximum likelihood estimates, the diagonal elements of `AVAR`

are
their asymptotic variances. `AVAR`

is based on the
observed Fisher's information, not the expected information.

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

accepts
a Boolean vector of the same size as `data`

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

`[...] = evlike(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 can contain any nonnegative values. Pass in `[]`

for `censoring`

to
use its default value.

The type 1 extreme value distribution is also known as the Gumbel
distribution. The version used here is suitable for modeling minima;
the mirror image of this distribution can be used to model maxima
by negating `data`

. See Extreme Value Distribution for more details. If *x* has
a Weibull distribution, then *X* = log(*x*)
has the type 1 extreme value distribution.

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