repl.txt (1849B)
1 2 {{alias}}( x, α, β ) 3 Evaluates the cumulative distribution function (CDF) for a gamma 4 distribution 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 CDF. 25 26 Examples 27 -------- 28 > var y = {{alias}}( 2.0, 1.0, 1.0 ) 29 ~0.865 30 > y = {{alias}}( 2.0, 3.0, 1.0 ) 31 ~0.323 32 > y = {{alias}}( -1.0, 2.0, 2.0 ) 33 0.0 34 > y = {{alias}}( {{alias:@stdlib/constants/float64/pinf}}, 4.0, 2.0 ) 35 1.0 36 > y = {{alias}}( {{alias:@stdlib/constants/float64/ninf}}, 4.0, 2.0 ) 37 0.0 38 39 > y = {{alias}}( NaN, 0.0, 1.0 ) 40 NaN 41 > y = {{alias}}( 0.0, NaN, 1.0 ) 42 NaN 43 > y = {{alias}}( 0.0, 0.0, NaN ) 44 NaN 45 46 > y = {{alias}}( 2.0, -1.0, 1.0 ) 47 NaN 48 > y = {{alias}}( 2.0, 1.0, -1.0 ) 49 NaN 50 51 // Degenerate distribution centered at `0` when `α = 0.0`: 52 > y = {{alias}}( 2.0, 0.0, 2.0 ) 53 1.0 54 > y = {{alias}}( -2.0, 0.0, 2.0 ) 55 0.0 56 > y = {{alias}}( 0.0, 0.0, 2.0 ) 57 0.0 58 59 60 {{alias}}.factory( α, β ) 61 Returns a function for evaluating the cumulative distribution function (CDF) 62 of a gamma distribution with shape parameter `α` and rate parameter `β`. 63 64 Parameters 65 ---------- 66 α: number 67 Shape parameter. 68 69 β: number 70 Rate parameter. 71 72 Returns 73 ------- 74 cdf: Function 75 Cumulative distribution function (CDF). 76 77 Examples 78 -------- 79 > var myCDF = {{alias}}.factory( 2.0, 0.5 ); 80 > var y = myCDF( 6.0 ) 81 ~0.801 82 > y = myCDF( 2.0 ) 83 ~0.264 84 85 See Also 86 -------- 87