# gfun

0th

Percentile

##### 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.

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

• gnorm
• glogis
• gcauchy
##### Examples
# NOT RUN {
x <- -5:5
gnorm(x)
glogis(x)
gcauchy(x)

# }

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

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