HYPGEOM_INV

Updated 2023-11-03 14:20:51.470000

Syntax

SELECT [westclintech].[wct].[HYPGEOM_INV](
  <@P, float,>
 ,<@Number_sample, float,>
 ,<@Population_s, float,>
 ,<@Number_population, float,>)

Description

Use the scalar function HYPGEOM_INV to calculate the quantiles of the hypergeometric distribution. The hypergeometric distribution is generally described using colored balls in an urn. Given an urn containing N balls of which K are white (and N-K are black), the hypergeometric distribution calculates the probability of drawing k white balls from a sample of n without replacement (meaning that once a ball is removed from the urn it is not put back).

Arguments

@Number_population

the size of the population. @Number_population must be of a type float or of a type that intrinsically converts to float.

@P

the probability value to be evaluated. @P must be of a type float or of type that intrinsically converts to float.

@Number_sample

the size of the sample. @Number_sample must be of a type float or of type that intrinsically converts to float.

@Population_s

the number of successes in the population. @Population_s must be of a type float or of type that intrinsically converts to float.

Return Type

float

Remarks

@Number_sample, @Population_s, and @Number_population are truncated; only the integer part is used.

0 ≤ @P ≤ 1.

0 ≤ @Population_s

0 < @Number_sample

0 < @Number_population

@Population_s ≤ @Number_population.

Examples

In an urn with 1000 balls of which 300 are white we want to calculate the number of while balls we should expect in a random sample of 25 balls 95% of the time.

SELECT wct.HYPGEOM_INV(   0.95, --@P

                          25,   --@Sample_s

                          300,  --@Population_s

                          1000  --@Number_Population

                      ) as HYPGEOM_INV;

This produces the following result.

{"columns":[{"field":"HYPGEOM_INV","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"HYPGEOM_INV":"11"}]}

In other words, in a random sample of 25 balls, we would expect to have no more than 11 white balls 95% of the time.