repl.txt (1542B)
1 2 {{alias}}( t, μ, β ) 3 Evaluates the moment-generating function (MGF) for a Gumbel distribution 4 with location parameter `μ` and scale parameter `β` at a value `t`. 5 6 If provided `NaN` as any argument, the function returns `NaN`. 7 8 If provided `β <= 0`, the function returns `NaN`. 9 10 Parameters 11 ---------- 12 t: number 13 Input value. 14 15 μ: number 16 Location parameter. 17 18 β: number 19 Scale parameter. 20 21 Returns 22 ------- 23 out: number 24 Evaluated MGF. 25 26 Examples 27 -------- 28 > var y = {{alias}}( -1.0, 0.0, 3.0 ) 29 6.0 30 > y = {{alias}}( 0.0, 0.0, 1.0 ) 31 1.0 32 > y = {{alias}}( 0.1, 0.0, 3.0 ) 33 ~1.298 34 35 > y = {{alias}}( NaN, 0.0, 1.0 ) 36 NaN 37 > y = {{alias}}( 0.0, NaN, 1.0 ) 38 NaN 39 > y = {{alias}}( 0.0, 0.0, NaN ) 40 NaN 41 42 // Case: `t >= 1/beta` 43 > y = {{alias}}( 0.8, 0.0, 2.0 ) 44 NaN 45 46 // Non-positive scale parameter: 47 > y = {{alias}}( 0.0, 0.0, -1.0 ) 48 NaN 49 50 51 {{alias}}.factory( μ, β ) 52 Returns a function for evaluating the moment-generating function (MGF) of a 53 Gumbel distribution with location parameter `μ` and scale parameter `β`. 54 55 Parameters 56 ---------- 57 μ: number 58 Location parameter. 59 60 β: number 61 Scale parameter. 62 63 Returns 64 ------- 65 mgf: Function 66 Moment-generating function (MGF). 67 68 Examples 69 -------- 70 > var myMGF = {{alias}}.factory( 0.0, 3.0 ); 71 > var y = myMGF( -1.5 ) 72 ~52.343 73 > y = myMGF( -1.0 ) 74 6.0 75 76 See Also 77 -------- 78