repl.txt (1550B)
1 2 {{alias}}( t, α, β ) 3 Evaluates the moment-generating function (MGF) for a gamma distribution with 4 shape parameter `α` and rate parameter `β` at a value `t`. 5 6 If `α <= 0` or `β <= 0`, the function returns `NaN`. 7 8 If `α` or `β` is `NaN`, the function returns `NaN`. 9 10 Parameters 11 ---------- 12 t: 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 MGF. 25 26 Examples 27 -------- 28 > var y = {{alias}}( 0.5, 0.5, 1.0 ) 29 ~1.414 30 > y = {{alias}}( 0.1, 1.0, 1.0 ) 31 ~1.111 32 > y = {{alias}}( -1.0, 4.0, 2.0 ) 33 ~0.198 34 35 > y = {{alias}}( NaN, 1.0, 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 > y = {{alias}}( 2.0, 4.0, 1.0 ) 43 NaN 44 > y = {{alias}}( 2.0, -0.5, 1.0 ) 45 NaN 46 > y = {{alias}}( 2.0, 1.0, 0.0 ) 47 NaN 48 > y = {{alias}}( 2.0, 1.0, -1.0 ) 49 NaN 50 51 52 {{alias}}.factory( α, β ) 53 Returns a function for evaluating the moment-generating function (MGF) of a 54 gamma distribution with shape parameter `α` and rate parameter `β`. 55 56 Parameters 57 ---------- 58 α: number 59 Shape parameter. 60 61 β: number 62 Rate parameter. 63 64 Returns 65 ------- 66 mgf: Function 67 Moment-generating function (MGF). 68 69 Examples 70 -------- 71 > var myMGF = {{alias}}.factory( 3.0, 1.5 ); 72 > var y = myMGF( 1.0 ) 73 ~27.0 74 > y = myMGF( 0.5 ) 75 ~3.375 76 77 See Also 78 -------- 79