repl.txt (1749B)
1 2 {{alias}}( x, α, β ) 3 Evaluates the logarithm of the probability density function (PDF) for a 4 gamma distribution with shape parameter `α` and rate parameter `β` at a 5 value `x`. 6 7 If `α < 0` or `β <= 0`, the function returns `NaN`. 8 9 If provided `NaN` as any argument, the function returns `NaN`. 10 11 Parameters 12 ---------- 13 x: number 14 Input value. 15 16 α: number 17 Shape parameter. 18 19 β: number 20 Rate parameter. 21 22 Returns 23 ------- 24 out: number 25 Evaluated logPDF. 26 27 Examples 28 -------- 29 > var y = {{alias}}( 2.0, 0.5, 1.0 ) 30 ~-2.919 31 > y = {{alias}}( 0.1, 1.0, 1.0 ) 32 ~-0.1 33 > y = {{alias}}( -1.0, 4.0, 2.0 ) 34 -Infinity 35 36 > y = {{alias}}( NaN, 0.6, 1.0 ) 37 NaN 38 > y = {{alias}}( 0.0, NaN, 1.0 ) 39 NaN 40 > y = {{alias}}( 0.0, 1.0, NaN ) 41 NaN 42 43 // Negative shape parameter: 44 > y = {{alias}}( 2.0, -1.0, 1.0 ) 45 NaN 46 // Non-positive rate parameter: 47 > y = {{alias}}( 2.0, 1.0, -1.0 ) 48 NaN 49 50 // Degenerate distribution centered at `0.0` when `α = 0.0`: 51 > y = {{alias}}( 2.0, 0.0, 2.0 ) 52 -Infinity 53 > y = {{alias}}( 0.0, 0.0, 2.0 ) 54 Infinity 55 56 57 {{alias}}.factory( α, β ) 58 Returns a function for evaluating the logarithm of the probability density 59 function (PDF) of a gamma distribution with shape parameter `α` and rate 60 parameter `β`. 61 62 Parameters 63 ---------- 64 α: number 65 Shape parameter. 66 67 β: number 68 Rate parameter. 69 70 Returns 71 ------- 72 logpdf: Function 73 Logarithm of probability density function (PDF). 74 75 Examples 76 -------- 77 > var mylogPDF = {{alias}}.factory( 6.0, 7.0 ); 78 > var y = mylogPDF( 2.0 ) 79 ~-3.646 80 81 See Also 82 -------- 83