@stdlib/stats
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Standard library statistical functions.
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{{alias}}( t, μ, β )
Evaluates the moment-generating function (MGF) for a Gumbel distribution
with location parameter `μ` and scale parameter `β` at a value `t`.
If provided `NaN` as any argument, the function returns `NaN`.
If provided `β <= 0`, the function returns `NaN`.
Parameters
----------
t: number
Input value.
μ: number
Location parameter.
β: number
Scale parameter.
Returns
-------
out: number
Evaluated MGF.
Examples
--------
> var y = {{alias}}( -1.0, 0.0, 3.0 )
6.0
> y = {{alias}}( 0.0, 0.0, 1.0 )
1.0
> y = {{alias}}( 0.1, 0.0, 3.0 )
~1.298
> y = {{alias}}( NaN, 0.0, 1.0 )
NaN
> y = {{alias}}( 0.0, NaN, 1.0 )
NaN
> y = {{alias}}( 0.0, 0.0, NaN )
NaN
// Case: `t >= 1/beta`
> y = {{alias}}( 0.8, 0.0, 2.0 )
NaN
// Non-positive scale parameter:
> y = {{alias}}( 0.0, 0.0, -1.0 )
NaN
{{alias}}.factory( μ, β )
Returns a function for evaluating the moment-generating function (MGF) of a
Gumbel distribution with location parameter `μ` and scale parameter `β`.
Parameters
----------
μ: number
Location parameter.
β: number
Scale parameter.
Returns
-------
mgf: Function
Moment-generating function (MGF).
Examples
--------
> var myMGF = {{alias}}.factory( 0.0, 3.0 );
> var y = myMGF( -1.5 )
~52.343
> y = myMGF( -1.0 )
6.0
See Also
--------