norminvp: Normal quantile function (high precision)
Description
Computes with tail-precision the quantile function
of the standard normal distribution at \(0\le p\le 1\),
and truncated to the interval \([l,u]\).
Infinite values for vectors \(l\) and \(u\) are accepted.
Usage
norminvp(p, l, u)
Value
quantile value of the truncated normal distribution.
Arguments
p
quantile at \(0\le p\le 1\)
l
lower truncation limit
u
upper truncation limit
Author
Zdravko I. Botev
Details
Suppose we wish to simulate a random variable \(Z\) drawn from \(N(\mu,\sigma^2)\) and
conditional on \(l<Z<u\) using the inverse transform method.
To achieve this, first compute
X=norminvp(runif(1),(l-mu)/sig,(u-mu)/sig) and then set
Z=mu+sig*X
References
Z. I. Botev (2017), The Normal Law Under Linear Restrictions:
Simulation and Estimation via Minimax Tilting, Journal of the Royal
Statistical Society, Series B, 79 (1), pp. 1--24.