POISSON

Updated 2024-03-13 13:20:23.237000

Syntax

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

Description

Use the scalar function POISSON to calculate the Poisson distribution. The formula for the probability mass function (pmf) is:

f(k; \lambda) = \Pr(X{=}k)= \frac{\lambda^k e^{-\lambda}}{k!}

where k is the number of occurrences and λ is the mean.

The formula for the cumulative distribution function (cdf) is:

F(k; \lambda) =Q(\lfloor{k+1}\rfloor,\lambda)

Where Q(a,x) is the regularized gamma function

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 number of events. @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.

Return Type

float

Remarks

@X is truncated to zero decimal places.

If @X < 0, POISSON returns an error.

If @Mean < 0, POISSON returns an error.

Examples

select wct.POISSON(2, 5, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0842243374885683"}]}

select wct.POISSON(2, 5, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.124652019483081"}]}