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).

Aliases
  • 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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