NORMDIST

Updated 2024-03-13 12:56:37.127000

Syntax

SELECT [westclintech].[wct].[NORMDIST] (
  <@X, float,>
 ,<@Mean, float,>
 ,<@Standard_dev, float,>
 ,<@Cumulative, bit,>)

Description

Use the scalar function NORMDIST to calculate the normal distribution for the specified mean and standard deviation. The formula for the probability density function (pdf) is:

f(x) = \frac{1}{\sigma \sqrt{2\pi} } e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

where μ is the mean and σ is the standard deviation.

The formula for the cumulative distribution function (cdf) 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

@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.

@X

is the value at which to evaluate the function. @X is an expression of type float or of a type that can be implicitly converted to float.

@Cumulative

is a logical value that determines if the probability density function (False, 0) or the cumulative distribution function (True, 1) is being calculated.

@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 @Standard_dev = 0, NORMDIST returns an error

If @Mean = 0 and @Standard_dev = 1 and @Cumulative = 'False', NORMDIST = NORMSDIST(@X)

Examples

Select wct.NORMDIST(-4.6159, 10, 5, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.00111280980994974"}]}

Select wct.NORMDIST(-4.6159, 10, 5, 'True');