LOGNORM_DIST
Updated 2023-11-03 21:04:59.847000
Syntax
SELECT [westclintech].[wct].[LOGNORM_DIST](
<@X, float,>
,<@Mean, float,>
,<@Standard_dev, float,>
,<@Cumulative, bit,>)
Description
Use the scalar function LOGNORM_DIST to calculate the probability density function or the cumulative distributive function of the normal distribution of x, when ln(x) is normally distributed with parameters µ and d.
Arguments
@Mean
the average of ln(x). @Mean must be of a type float or of type that intrinsically converts to float.
@X
the value of interest. @X must be of a type float or of type that intrinsically converts to float.
@Cumulative
a bit value identifying whether the probability density 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.
@Standard_dev
the standard deviation of ln(x). @Standard_dev must be of a type float or of type that intrinsically converts to float.
Return Type
float
Remarks
0 < @X.
0 < @Standard_dev.
Examples
Calculate the lognormal distribution with x = 4 and the mean of ln(x) = 3.5 and the standard deviation of ln(x) = 1.2
SELECT wct.LOGNORM_DIST( 4, --@X
3.5, --@Mean
1.2, --@Standard_dev
'False' --@Cumulative
) as pdf;
This produces the following result.
{"columns":[{"field":"pdf","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"pdf":"0.0176175966818192"}]}
In this example we calculate the cumulative distribution function.
SELECT wct.LOGNORM_DIST( 4, --@X
3.5, --@Mean
1.2, --@Standard_dev
'True' --@Cumulative
) as cdf;
This produces the following result.
{"columns":[{"field":"cdf","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"cdf":"0.0390835557068005"}]}
The lognormal distribution is related to the standard normal distribution.
SELECT wct.LOGNORM_DIST(x, mu, sigma, 'True') as cdf,
wct.NORM_S_DIST((log(x) - mu) / sigma, 'True') as cdf
FROM
(
VALUES
(4, 3.5, 1.2)
) n (x, mu, sigma);
This produces the following result.
{"columns":[{"field":"cdf","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"cdf","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"cdf":"0.0390835557068005"}]}