gfun {ordinal}

Gradients of common densities

Description

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.

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.

Author(s)

Rune Haubo B Christensen

See Also

Gradients of densities are also implemented for the extreme value distribtion (gumbel) and the the log-gamma distribution (log-gamma).

Examples

x <- -5:5
gnorm(x)
glogis(x)
gcauchy(x)