NEGBINOMDIST

Updated 2024-03-12 20:51:51.710000

Syntax

SELECT [westclintech].[wct].[NEGBINOMDIST] (
   <@Number_f, float,>
 ,<@Number_s, float,>
 ,<@Probability_s, float,>)

Description

Use the scalar function NEGBINOMDIST to calculate the negative binomial distribution. NEGBINOMDIST returns the probability that there will be k failures before the rth success, when the constant probability of a success is p. The formula for the probability mass function of the negative binomial distribution is:

f(k; r, p) \equiv \Pr(X = k) = \binom{k+r-1}{k} (1-p)^k p^r

Where

{
    "columns": [
        {
            "field": "column 1",
            "maxWidth": 100
        },
        {
            "field": "column 2",
            "maxWidth": 325
        }
    ],
    "rows": [
        {
            "column 1": "k",
            "column 2": "is the number of failures"
        },
        {
            "column 1": "r",
            "column 2": "is the number of successes"
        },
        {
            "column 1": "p",
            "column 2": "is the probability of a success"
        }
    ]
}

Arguments

@Number_f

is the number of failures. @Number_f is an expression of type float or of a type that can be implicitly converted to float.

@Number_s

is the number of successes. @Number_s is an expression of type float or of a type that can be implicitly converted to float.

@Probability_s

is the probability of a success. @Probability_s is an expression of type float or of a type that can be implicitly converted to float.

Return Type

float

Remarks

If @Probability_s <0 or @Probability_s > 1, NEGBINOMDIST returns an error.

If @Number_f < 0 or @Number_s < 1, NEGBINOMDIST returns an error.

NEGBINOMDIST = BINOMDIST(@Number_s, @Number_f + @Number_s, @Probability, 'False') * @Number_s / (@Number_f + @Number_s)

Examples

SELECT wct.NEGBINOMDIST(4, 90, 0.975);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.116820452331376"}]}

SELECT wct.BINOMDIST(90, 90 + 4, 0.975, 'False') * 90 / (90 + 4);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.116820452331368"}]}

select wct.BETADIST(0.975, 90, 4 + 1, NULL, NULL) - wct.BETADIST(0.975, 90, 4, 

          NULL, NULL);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.116820452331374"}]}