dapprox_unif {sdPrior}

Compute Density Function of Approximated (Differentiably) Uniform Distribution.

Description

Compute Density Function of Approximated (Differentiably) Uniform Distribution.

Usage

dapprox_unif(x, scale, tildec = 13.86294)

Arguments

x

denotes the argument of the density function.

scale

the scale parameter originally defining the upper bound of the uniform distribution.

tildec

denotes the ratio between scale parameter \theta and s. The latter is responsible for the closeness of the approximation to the uniform distribution. See also below for further details and the default value.

Details

The density of the uniform distribution for \tau is approximated by

p(\tau)=(1/(1+exp(\tau\tilde{c}/\theta-\tilde{c})))/(\theta(1+log(1+exp(-\tilde{c}))))

. This results in

p(\tau^2)=0.5*(\tau^2)^(-1/2)(1/(1+exp((\tau^2)^(1/2)\tilde{c}/\theta-\tilde{c})))/(\theta(1+log(1+exp(-\tilde{c}))))

for tau^2. \tilde{c} is chosen such that P(\tau<=\theta)>=0.95.

Value

the density.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

See Also

rapprox_unif,papprox_unif