# gfun

##### Gradients of common densities

Gradients of common density functions in their standard forms, i.e.,
with zero location (mean) and unit scale. These are implemented in C
for speed and care is taken that the correct results are provided for
the argument being `NA`

, `NaN`

, `Inf`

, `-Inf`

or
just extremely small or large.

- Keywords
- distribution

##### Usage

`gnorm(x)`glogis(x)

gcauchy(x)

##### Arguments

- x
numeric vector of quantiles.

##### Details

The gradients are given by:

gnorm: If \(f(x)\) is the normal density with mean 0 and spread 1, then the gradient is $$f'(x) = -x f(x)$$

glogis: If \(f(x)\) is the logistic density with mean 0 and scale 1, then the gradient is $$f'(x) = 2 \exp(-x)^2 (1 + \exp(-x))^{-3} - \exp(-x)(1+\exp(-x))^{-2}$$

pcauchy: If \(f(x) = [\pi(1 + x^2)^2]^{-1}\) is the cauchy density with mean 0 and scale 1, then the gradient is $$f'(x) = -2x [\pi(1 + x^2)^2]^{-1}$$

These gradients are used in the Newton-Raphson algorithms in fitting
cumulative link models with `clm`

and cumulative link
mixed models with `clmm`

.

##### Value

a numeric vector of gradients.

##### See Also

Gradients of densities are also implemented for the extreme value
distribtion (`gumbel`

) and the the log-gamma distribution
(`log-gamma`

).

##### Examples

```
# NOT RUN {
x <- -5:5
gnorm(x)
glogis(x)
gcauchy(x)
# }
```

*Documentation reproduced from package ordinal, version 2019.12-10, License: GPL (>= 2)*