repl.txt (1667B)
1 2 {{alias}}( t, α, β ) 3 Evaluates the moment-generating function (MGF) for a beta distribution with 4 first shape parameter `α` and second shape parameter `β` at a value `t`. 5 6 If provided `NaN` as any argument, the function returns `NaN`. 7 8 If `α <= 0` or `β <= 0`, the function returns `NaN`. 9 10 Parameters 11 ---------- 12 t: number 13 Input value. 14 15 α: number 16 First shape parameter. 17 18 β: number 19 Second shape parameter. 20 21 Returns 22 ------- 23 out: number 24 Evaluated MGF. 25 26 Examples 27 -------- 28 > var y = {{alias}}( 0.5, 1.0, 1.0 ) 29 ~1.297 30 > y = {{alias}}( 0.5, 2.0, 4.0 ) 31 ~1.186 32 > y = {{alias}}( 3.0, 2.0, 2.0 ) 33 ~5.575 34 > y = {{alias}}( -0.8, 4.0, 4.0 ) 35 ~0.676 36 37 > y = {{alias}}( NaN, 1.0, 1.0 ) 38 NaN 39 > y = {{alias}}( 0.0, NaN, 1.0 ) 40 NaN 41 > y = {{alias}}( 0.0, 1.0, NaN ) 42 NaN 43 44 > y = {{alias}}( 2.0, -1.0, 0.5 ) 45 NaN 46 > y = {{alias}}( 2.0, 0.0, 0.5 ) 47 NaN 48 49 > y = {{alias}}( 2.0, 0.5, -1.0 ) 50 NaN 51 > y = {{alias}}( 2.0, 0.5, 0.0 ) 52 NaN 53 54 55 {{alias}}.factory( α, β ) 56 Returns a function for evaluating the moment-generating function (MGF) of a 57 beta distribution with first shape parameter `α` and second shape parameter 58 `β`. 59 60 Parameters 61 ---------- 62 α: number 63 First shape parameter. 64 65 β: number 66 Second shape parameter. 67 68 Returns 69 ------- 70 mgf: Function 71 Moment-generating function (MGF). 72 73 Examples 74 -------- 75 > var myMGF = {{alias}}.factory( 0.5, 0.5 ); 76 > var y = myMGF( 0.8 ) 77 ~1.552 78 > y = myMGF( 0.3 ) 79 ~1.168 80 81 See Also 82 -------- 83