normal.quantile

normal.quantile, function

def pure normal.quantile(mu: number, sigma: number, p: number): number

Returns the quantile of probability p for the normal distribution with mean mu and standard deviation sigma.

• mu: the mean of the normal distribution.
• sigma: the standard deviation of the normal distribution, which must be non-negative.
• p: the cumulative probability, which must be strictly between 0 and 1.

Examples

table T = with
  [| as Mu, as Sigma, as P |]
  [| 0, 1, 0.15865526 |]
  [| 0, 1, 0.8413447  |]
  [| 10, 2, 0.8413447 |]
  [| 10, 0, 0.25      |]

show table "normal.quantile" with
  T.Mu
  T.Sigma
  T.P
  normal.quantile(T.Mu, T.Sigma, T.P) as "Quantile"

This outputs the following table:

Remarks

When sigma is zero, normal.quantile(mu, 0, p) always returns mu for any valid p.

For sigma > 0, normal.quantile is the inverse of normal.cdf up to numerical precision.

Errors

Calling normal.quantile with a negative sigma results in an error message:

’normal.quantile()’: sigma must be non-negative, but found -1.

Calling normal.quantile with p <= 0 or p >= 1 results in an error message:

’normal.quantile(mu,sigma,p)’ : invalid value 1 for p, should be in ]0, 1[.

See also

• normal
• normal.cdf
• quantile