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