EXPONDIST

Updated 2024-03-07 21:36:52.537000

Syntax

SELECT [westclintech].[wct].[EXPONDIST] (
  <@X, float,>
 ,<@Lambda, float,>
 ,<@Cumulative, bit,>)

Description

Use the scalar function EXPONDIST to calculate an exponential distribution that is equivalent to the function used in EXCEL. Exponential distributions describe times between events in a Poisson process, i.e., a process in which events occur continuously and independently at a constant average rate.

The equation for the probability density function is:

f(x;\lambda)=\lambda{e}^{-\lambda{x}}

The equation for the cumulative distribution function is:

F(x;\lambda)=1-{e}^{-\lambda{x}}

Arguments

@Cumulative

is a logical value that determines the probability density function (False, 0) or the cumulative distribution function (True, 1) is being calculated.

@X

is the value of the function. @X is an expression of type float or of a type that can be implicitly converted to float.

@Lambda

is the parameter value. @Lambda is an expression of type float or of a type that can be implicitly converted to float.

Return Type

float

Remarks

If @X < 0, EXPONDIST returns an error.

If @Lambda = 0, EXPONDIST returns an error.

EXPONDIST = GAMMADIST(@X,1,1/@Lambda, @Cumulative).

EXPONDIST = WEIBULL(@X,1,1/@Lambda, @Cumulative).

Examples

select wct.EXPONDIST(0.5, 9.5, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.082191104429646"}]}

select wct.GAMMADIST(0.5, 1, 1.0000000 / 9.50000000, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0821911044296461"}]}

select wct.EXPONDIST(0.5, 9.5, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.991348304796879"}]}

select wct.GAMMADIST(0.5, 1, 1.0000000 / 9.50000000, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.991348304796879"}]}