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.
gnorm(x) glogis(x) gcauchy(x)
x |
numeric vector of quantiles. |
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) =1 / [pi (1 + x^2)^2] is the cauchy density with mean 0 and scale 1, then the gradient is
f'(x) = -2x / [pi (1 + x^2)^2]
a numeric vector of gradients.
Rune Haubo B Christensen
x <- -5:5 gnorm(x) glogis(x) gcauchy(x)
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