RANDCAUCHY

Updated 2023-10-18 15:36:31.553000

Syntax

SELECT * FROM [westclintech].[wct].[RANDCAUCHY](
  <@Rows, int,>
 ,<@mu, float,>
 ,<@sig, float,>)

Description

Use the table-valued function RANDCAUCHY to generate a sequence of random numbers from a Cauchy distribution with locations @mu and scale @sig.

Arguments

@mu

the location parameter. @mu 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.

@sig

the scale parameter. @sig 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": "6a8b7a40-c4f5-4e54-9bf5-fff81619752d", "colName": "Seq", "colDatatype": "int", "colDesc": "A monotonically increasing sequence number"}, {"id": "3f2dfeee-bba2-4a52-8b01-2badba6d56d9", "colName": "X", "colDatatype": "float", "colDesc": "The random variable"}]}

Remarks

@sig must be greater than zero.

If @mu is NULL then @mu is set to 0.

If @sig is NULL then @sig 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 Cauchy distribution with @mu = 0 and @sig = 1, COUNT the results, paste them into Excel where the values are between -10 and 10 and graph them.

SELECT X,
       COUNT(*) as COUNT
FROM
(
    SELECT ROUND(X, 1) as X
    FROM wct.RANDCAUCHY(   1000000, --@Rows
                           0,       --@mu
                           1        --@sig
                       )
) n
WHERE X
BETWEEN -10 AND 10
GROUP BY X
ORDER BY 1;

This produces the following result.