Statistical.NormInv

Returns the inverse of the cumulative distribution function (CDF) of the normal distribution.

Syntax

Statistical.NormInv(
    probability as number,
    optional mean as number,
    optional sd as number
) as number

Parameters

• probability: A probability value between 0 and 1. Values outside this range are clamped to 0 or 1.
• mean (optional): The mean ($\mu$) of the distribution. Defaults to 0 if not provided.
• standard deviation (optional): The standard deviation ($\sigma$) of the distribution. Defaults to 1 if not provided.

Return Value

A number representing the value $x$ such that the normal distribution's cumulative probability $P(X \le x)$ equals the given probability. If neither mean nor standard deviation are specified, returns the value $z$ such that the standard normal distribution's cumulative probability $P(Z \le z)$ equals the given probability.

Remarks

• The function uses a rational approximation algorithm to compute the inverse of the standard normal distribution.
• The input probability is clamped between 0 and 1. Values outside this range are adjusted to the nearest valid bound.
• For probability = 0, the result is negative infinity (Number.NegativeInfinity).
• For probability = 1, the result is positive infinity (Number.PositiveInfinity).

Examples

Example 1: Returns $x$ such that $P(X \le x) = p$ for a normal distribution with given mean and standard deviation.

Statistical.NormInv(0.9, 100, 15)

Result

119.22327346210234

Example 2: If neither mean nor standard deviation are informed, returns the value $z$ such that $P(Z \le z) = p$ under the standard normal distribution.

Statistical.NormInv(0.9)

Result

1.2815515641401563

Credits

• An algorithm for computing the inverse normal cumulative distribution function
  • Author: Peter John Acklam
  • Original Site: http://home.online.no/~pjacklam/notes/invnorm
  • Published at: May 4th, 2003