norminvp function

Normal quantile function (high precision)

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.

norminvp(p, l, u)

Arguments

• p: quantile at $0\le p\le 1$
• l: lower truncation limit
• u: upper truncation limit

Returns

quantile value of the truncated normal distribution.

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

Note

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.

Examples

d <- 150 # simulate via inverse transform method
 norminvp(runif(d),l = 1:d, u = rep(Inf, d))

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.

See Also

trandn

Author(s)

Zdravko I. Botev