SQL Server RANDGAMMA Function

Updated 2023-10-18 15:55:38.437000

Description

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

Syntax

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

Arguments

@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.

@Scale

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

Return Type

table

colName	colDatatype	colDesc
Seq	int	A monotonically increasing sequence number
X	float	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).

stat	RANDGAMMA	EXPECTED
avg	10.0025412937376	10
kurt	1.18154165719261	1.2
skew	0.892342912517966	0.894427190999916
stdev	4.47160145369588	4.47213595499958