Normal quantile function (high precision)
Computes with tail-precision the quantile function of the standard normal distribution at 0≤ p≤ 1, and truncated to the interval [l,u]. Infinite values for vectors l and u are accepted.
norminvp(p, l, u)
p |
quantile at 0≤ p≤ 1 |
l |
lower truncation limit |
u |
upper truncation limit |
Suppose we wish to simulate a random variable Z drawn from N(μ,σ^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
quantile value of the truncated normal distribution.
If you wish to simulate truncated normal variables fast, use trandn.
Using norminvp is advisable only when needed, for example,
in quasi-Monte Carlo or antithetic sampling, where the inverse transform method
is unavoidable.
Zdravko I. Botev
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.
d <- 150 # simulate via inverse transform method norminvp(runif(d),l = 1:d, u = rep(Inf, d))
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