NEGHYPGEOM_DIST

Updated 2024-03-13 12:33:12.017000

Syntax

SELECT [westclintech].[wct].[NEGHYPGEOM_DIST](
  <@num_trials, float,>
 ,<@num_success, float,>
 ,<@pop_success, float,>
 ,<@pop_size, float,>
 ,<@Cumulative, bit,>)

Description

Use the scalar function NEGHYPGEOM_DIST to calculate the probability mass function or the cumulative distributive function of the negative hypergeometric distribution. The negative hypergeometric distribution models the sample size required to achieve a specified number of failures given the number of successes and the size of the population. The probability mass function can be calculated as:

P(x)=\frac{\binom{x-1}{k-1}\binom{N-x}{M-k}}{\binom{N}{M}};k\leq{x}\leq{k+N-M}

Where:

{"columns":[{"field":"column 1",
            "maxWidth": 25},{"field":"column 2",
            "maxWidth": 25},{"field":"column 3",
            "maxWidth": 600,"wrapText":"true","autoHeight": "true"}],"rows":[{"column 1":"x","column 2":"=","column 3":"number of trials"},{"column 1":"M","column 2":"=","column 3":"number of successes in the population"},{"column 1":"N","column 2":"=","column 3":"population size"},{"column 1":"k","column 2":"=","column 3":"number of successes to achieve with the sample"}]}

The cumulative distribution function can be calculated as:

cdf=\sum_{x=k}^{num\_trials}\frac{\binom{x-1}{k-1}\binom{N-x}{M-k}}{\binom{N}{M}};k\leq{x}\leq{k+N-M}

Arguments

@Cumulative

a bit value identifying whether the probability mass function ( 'False') or the cumulative distribution function ( 'True') is to be returned. @Cumulative is of a type bit or a type that implicitly converts to bit.

@num_trials

the number of trials until @num_success have occurred. @num_trials must be of a type float or of type that intrinsically converts to float.

@num_success

the number of successes to achieve with the sample. @num_success must be of a type float or of type that intrinsically converts to float.

@pop_success

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

@pop_size

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

Return Type

float

Remarks

@num_trials, @num_success, @pop_success, and @pop_size are truncated; only the integer part is used.

If @num_success < 0 then NULL is returned.

If @pop_success < 0 then NULL is returned.

If @num_trials = 0 then NULL is returned.

If @pop_size = 0 then NULL is returned.

If @pop_success > @pop_size then NULL is returned.

If @num_trials > @pop_size - @pop_success + @num_success then NULL is returned.

Examples

In an urn with 1000 balls of which 300 are white we want to calculate the probability of drawing exactly 40 white balls in 150 draws from the urn.

SELECT wct.NEGHYPGEOM_DIST(   150,    --@num_trials

                              40,     --@num_success

                              300,    --@pop_success

                              1000,   --@pop_size

                              'False' --@Cumulative

                          ) as NEGHYPGEOM_DIST;