repl.txt (1669B)
1 2 {{alias}}( x, α, β ) 3 Evaluates the probability density function (PDF) for a gamma distribution 4 with shape parameter `α` and rate parameter `β` at a value `x`. 5 6 If `α < 0` or `β <= 0`, the function returns `NaN`. 7 8 If provided `NaN` as any argument, the function returns `NaN`. 9 10 Parameters 11 ---------- 12 x: number 13 Input value. 14 15 α: number 16 Shape parameter. 17 18 β: number 19 Rate parameter. 20 21 Returns 22 ------- 23 out: number 24 Evaluated PDF. 25 26 Examples 27 -------- 28 > var y = {{alias}}( 2.0, 0.5, 1.0 ) 29 ~0.054 30 > y = {{alias}}( 0.1, 1.0, 1.0 ) 31 ~0.905 32 > y = {{alias}}( -1.0, 4.0, 2.0 ) 33 0.0 34 35 > y = {{alias}}( NaN, 0.6, 1.0 ) 36 NaN 37 > y = {{alias}}( 0.0, NaN, 1.0 ) 38 NaN 39 > y = {{alias}}( 0.0, 1.0, NaN ) 40 NaN 41 42 // Negative shape parameter: 43 > y = {{alias}}( 2.0, -1.0, 1.0 ) 44 NaN 45 // Non-positive rate parameter: 46 > y = {{alias}}( 2.0, 1.0, -1.0 ) 47 NaN 48 49 // Degenerate distribution centered at `0.0` when `α = 0.0`: 50 > y = {{alias}}( 2.0, 0.0, 2.0 ) 51 0.0 52 > y = {{alias}}( 0.0, 0.0, 2.0 ) 53 Infinity 54 55 56 {{alias}}.factory( α, β ) 57 Returns a function for evaluating the probability density function (PDF) of 58 a gamma distribution with shape parameter `α` and rate parameter `β`. 59 60 Parameters 61 ---------- 62 α: number 63 Shape parameter. 64 65 β: number 66 Rate parameter. 67 68 Returns 69 ------- 70 pdf: Function 71 Probability density function (PDF). 72 73 Examples 74 -------- 75 > var myPDF = {{alias}}.factory( 6.0, 7.0 ); 76 > var y = myPDF( 2.0 ) 77 ~0.026 78 79 See Also 80 -------- 81