papprox_unif: Compute Cumulative Distribution Function of Approximated (Differentiably) Uniform Distribution.
Description
Compute Cumulative Distribution Function of Approximated (Differentiably) Uniform Distribution.Usage
papprox_unif(x, scale, tildec = 13.86294)
Value
- the cumulative distribution function.
Details
The cumulative distribution function of dapprox_unif is given by
$$(1/(log(1+exp(-\tilde{c}))+\tilde{c}))*(\tilde{c}*(\tau^2)^(1/2)/\theta-log(exp((\tau^2)^(1/2)*\tilde{c}/\theta)+exp(\tilde{c})))$$
$\tilde{c}$ is chosen such that $P(\tau^2<=\theta)>=0.95$.References
Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression.
Working Paper.