RANDGAMMA

Updated 2023-10-18 15:55:38.437000

Syntax

SELECT * FROM [westclintech].[wct].[RANDGAMMA](
  <@Rows, int,>
 ,<@Shape, float,>
 ,<@Scale, float,>)

Description

Use the table-valued function RANDGAMMA to generate a sequence of random numbers from a gamma distribution with parameters @Shape and @Scale.

Arguments

@Scale

the scale parameter. @Scale must be of the type float or of a type that implicitly converts to float.

@Rows

the number of rows to generate. @Rows must be of the type int or of a type that implicitly converts to int.

@Shape

the shape parameter. @Shape must be of the type float or of a type that implicitly converts to float.

Return Type

table

{"columns": [{"field": "colName", "headerName": "Name", "header": "name"}, {"field": "colDatatype", "headerName": "Type", "header": "type"}, {"field": "colDesc", "headerName": "Description", "header": "description", "minWidth": 1000}], "rows": [{"id": "bfa395df-6be4-46d2-835b-c0ebad3f5538", "colName": "Seq", "colDatatype": "int", "colDesc": "A monotonically increasing sequence number"}, {"id": "9244da76-8813-4f0a-bbad-bcd6d0e34584", "colName": "X", "colDatatype": "float", "colDesc": "The random variable"}]}

Remarks

@Shape must be greater than zero.

@Scale must be greater than zero.

If @Shape is NULL then @Shape is set to 1.

If @Scale is NULL then @Scale is set to 1.

If @Rows is less than 1 then no rows are returned.

Examples

In this example we create a sequence 1,000,000 random numbers rounded to one decimal place from a gamma distribution with @Shape = 9 and @Scale = 0, COUNT the results, paste them into Excel, and graph them.

SELECT X,

       COUNT(*) as [COUNT]

FROM

(

    SELECT ROUND(X, 1) as X

    FROM wct.RANDGAMMA(   1000000, --@Rows

                          9,       --@Shape

                          0.5      --@Scale

                      )

) n

GROUP BY X

ORDER BY X;

This produces the following result.

In this example we generate 1,000,000 random numbers from a gamma distribution with @Shape of 5 and @Scale of 2. We calculate the mean, standard deviation, skewness, and excess kurtosis from the resultant table and compare those values to the expected values for the distribution.

DECLARE @size as int = 1000000;

DECLARE @Shape as float = 5;

DECLARE @scale as float = 2;

DECLARE @mean as float = @Shape * @Scale;

DECLARE @var as float = @Shape * POWER(@Scale, 2);

DECLARE @stdev as float = SQRT(@var);

DECLARE @skew as float = 2 / SQRT(@Shape);

DECLARE @kurt as float = 6e+00 / @Shape;

SELECT stat,

       [RANDGAMMA],

       [EXPECTED]

FROM

(

    SELECT x.*

    FROM

    (

        SELECT MIN(x) as min_GAMMA,

               AVG(x) as mean_GAMMA,

               MAX(x) as max_GAMMA,

               STDEVP(x) as stdev_GAMMA,

               wct.SKEWNESS_P(x) as skew_GAMMA,

               wct.KURTOSIS_P(x) as kurt_GAMMA

        FROM wct.RANDGAMMA(@size, @Shape, @scale)

    ) n

        CROSS APPLY

    (

        VALUES

            ('RANDGAMMA', 'avg', mean_GAMMA),

            ('RANDGAMMA', 'stdev', stdev_GAMMA),

            ('RANDGAMMA', 'skew', skew_GAMMA),

            ('RANDGAMMA', 'kurt', kurt_GAMMA),

            ('EXPECTED', 'avg', @mean),

            ('EXPECTED', 'stdev', @stdev),

            ('EXPECTED', 'skew', @skew),

            ('EXPECTED', 'kurt', @kurt)

    ) x (fn_name, stat, val_stat)

) d

PIVOT

(

    sum(val_stat)

    FOR fn_name in ([RANDGAMMA], [EXPECTED])

) P;

This produces the following result (your result will be different).

{"columns":[{"field":"stat"},{"field":"RANDGAMMA","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"EXPECTED","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"stat":"avg","RANDGAMMA":"10.0025412937376","EXPECTED":"10"},{"stat":"kurt","RANDGAMMA":"1.18154165719261","EXPECTED":"1.2"},{"stat":"skew","RANDGAMMA":"0.892342912517966","EXPECTED":"0.894427190999916"},{"stat":"stdev","RANDGAMMA":"4.47160145369588","EXPECTED":"4.47213595499958"}]}