88 lines
1.8 KiB
Plaintext
88 lines
1.8 KiB
Plaintext
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{{alias}}( x, α, β )
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Evaluates the cumulative distribution function (CDF) for a gamma
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distribution with shape parameter `α` and rate parameter `β` at a value `x`.
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If `α < 0` or `β <= 0`, the function returns `NaN`.
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If provided `NaN` as any argument, the function returns `NaN`.
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Parameters
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----------
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x: number
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Input value.
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α: number
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Shape parameter.
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β: number
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Rate parameter.
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Returns
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-------
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out: number
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Evaluated CDF.
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Examples
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--------
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> var y = {{alias}}( 2.0, 1.0, 1.0 )
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~0.865
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> y = {{alias}}( 2.0, 3.0, 1.0 )
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~0.323
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> y = {{alias}}( -1.0, 2.0, 2.0 )
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0.0
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> y = {{alias}}( {{alias:@stdlib/constants/float64/pinf}}, 4.0, 2.0 )
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1.0
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> y = {{alias}}( {{alias:@stdlib/constants/float64/ninf}}, 4.0, 2.0 )
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0.0
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> y = {{alias}}( NaN, 0.0, 1.0 )
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NaN
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> y = {{alias}}( 0.0, NaN, 1.0 )
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NaN
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> y = {{alias}}( 0.0, 0.0, NaN )
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NaN
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> y = {{alias}}( 2.0, -1.0, 1.0 )
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NaN
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> y = {{alias}}( 2.0, 1.0, -1.0 )
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NaN
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// Degenerate distribution centered at `0` when `α = 0.0`:
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> y = {{alias}}( 2.0, 0.0, 2.0 )
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1.0
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> y = {{alias}}( -2.0, 0.0, 2.0 )
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0.0
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> y = {{alias}}( 0.0, 0.0, 2.0 )
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0.0
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{{alias}}.factory( α, β )
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Returns a function for evaluating the cumulative distribution function (CDF)
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of a gamma distribution with shape parameter `α` and rate parameter `β`.
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Parameters
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----------
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α: number
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Shape parameter.
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β: number
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Rate parameter.
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Returns
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-------
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cdf: Function
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Cumulative distribution function (CDF).
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Examples
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--------
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> var myCDF = {{alias}}.factory( 2.0, 0.5 );
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> var y = myCDF( 6.0 )
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~0.801
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> y = myCDF( 2.0 )
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~0.264
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See Also
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--------
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