LOGINV

Updated 2023-11-03 20:59:30.887000

Syntax

SELECT [westclintech].[wct].[LOGINV] (
   <@Probability, float,>
 ,<@Mean, float,>
 ,<@Standard_dev, float,>)

Description

Use the scalar function LOGINV to calculate the inverse of the lognormal cumulative distribution function of x where ln(x) is normally distributed within the parameters mean and standard deviation.

Arguments

@Probability

is a probability associated with the lognormal distribution. @Probability is an expression of type float or of a type that can be implicitly converted to float.

@Mean

is the mean of ln(x). @Mean is an expression of type float or of a type that can be implicitly converted to float.

@Standard_dev

is the standard deviation of ln(x). @Standard_dev is an expression of type float or of a type that can be implicitly converted to float.

Return Type

float

Remarks

If @Probability < 0 or @Probability > 1, LOGINV returns an error

If @Standard_dev = 0, LOGINV returns an error

LOGNORMDIST(LOGINV(@Probability, @Mean, @Standard_dev), @Mean, @Standard_dev) - @Probability = 0 rounded to 8 decimal places.

Examples

select wct.LOGINV(0.025765031270143, 5, 1.5);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"8"}]}

Select round(wct.LOGNORMDIST(wct.LOGINV(0.025765031270143, 5, 1.5), 5, 1.5) - 

          0.025765031270143, 9);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0"}]}

Select EXP(5 + 1.5 * wct.NORMSINV(0.025765031270143));

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"8"}]}