NORMINV

Updated 2024-03-13 12:57:23.460000

Syntax

SELECT [westclintech].[wct].[NORMINV] (
  <@Probability, float,>
 ,<@Mean, float,>
 ,<@Standard_dev, float,>)

Description

Use the scalar function NORMINV to calculate the inverse of the normal cumulative distribution function (cdf). The formula for cumulative distribution function is:

\Phi_{\mu,\sigma^2}(x) = \frac 1 {\sigma\sqrt{2\pi}} \int_{-\infty}^x e^{\frac{-(u-\mu)^2}{2\sigma^2}} \, du

Arguments

@Probability

is a probability corresponding to the normal distribution. @Probability is an expression of type float or of a type that can be implicitly converted to float.

@Mean

is the arithmetic mean of the distribution. @Mean is an expression of type float or of a type that can be implicitly converted to float.

@Standard_dev

is the standard deviation of the distribution. @Standard_dev is an expression of type float or of a type that can be implicitly converted to float.

Return Type

float

Remarks

If @Probability < 0 or @Probability > 1, NORMINV returns an error.

If @Standard_dev = 0, NORMINV returns an error.

If @Mean = 0 and @Standard_dev = 1, NORMINV = NORMSINV(@Probability).

NORMINV uses root-finding algorithms and iteration to solve for NORMDIST(NORMINV(@Probability, @Mean, @Standard_dev), @Mean, @Standard_dev,'True') - @Probability = 0 to eight decimal places.

Examples

Select wct.NORMINV(0.00173238078965338, 10, 5);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"-4.61589999992911"}]}

Select Round(wct.NORMDIST(wct.NORMINV(0.00173238078965338, 10, 5), 10, 5, 'True')

          - 0.00173238078965338, 9);