/usr/share/openturns/validation/ValidInverseNatafCopula2.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 | > restart:
> Digits:=20:
> with(Statistics):
> G:=RandomVariable(Normal(0,1)):
> X1:=RandomVariable(Uniform(-1,2)):
> CDF1:=CDF(X1,x1);
> X2:=RandomVariable(Gamma(1/2,2)):
> CDF2:=CDF(X2,x2);
> X3:=RandomVariable(Beta(r,t-r)):
> CDF3:=subs(t3=((x3+1)/3),r=2,t=5,CDF(X3,t3));
{ 0 x1 < -1
{
{ x1
CDF1 := { 1/3 + ---- x1 < 2
{ 3
{
{ 1 otherwise
{ 0 x2 <= 0
CDF2 := {
{ -exp(-2 x2) - 2 exp(-2 x2) x2 + 1 0 < x2
{
{
CDF3 := { x3
{ 0 , ---- < -1/3
{ 3
/ x3 \2 x3
|---- + 1/3| hypergeom([2, -2], [3], ---- + 1/3)
\ 3 / 3
1/2 ------------------------------------------------- ,
Beta(2, 3)
x3
---- < 2/3
3
1 , otherwise
> X1:=evalf(subs(subs(x1=1,CDF1)));
> X2:=evalf(subs(subs(x2=1,CDF2)));
> X3:=evalf(subs(subs(x3=1,CDF3)));
X1 := 0.66666666666666666667
X2 := 0.59399415029016192433
X3 := 0.88888888888888888889
> u1:=fsolve(CDF(G,x)=X1,x);
> u2:=fsolve(CDF(G,x)=X2,x);
> u3:=fsolve(CDF(G,x)=X3,x);
u1 := 0.43072729929545749022
u2 := 0.23783161172327289985
u3 := 1.2206403488473496983
> INEC_g1:=evalf(subs(x=u1,PDF(G,x)));
> INEC_g2:=evalf(subs(x=u2,PDF(G,x)));
> INEC_g3:=evalf(subs(x=u3,PDF(G,x)));
INEC_g1 := 0.36359977467531772230
INEC_g2 := 0.38781747667892138429
INEC_g3 := 0.18939510112030681087
> INEC_h1:=evalf(subs(x=u1,diff(PDF(G,x),x)));
> INEC_h2:=evalf(subs(x=u2,diff(PDF(G,x),x)));
> INEC_h3:=evalf(subs(x=u3,diff(PDF(G,x),x)));
INEC_h1 := -0.15661234897033648136
INEC_h2 := -0.092235255533000673534
INEC_h3 := -0.23118330230147037728
> IMT_g1:=1/evalf(subs(x1=1,diff(CDF1,x1)));
> IMT_g2:=1/evalf(subs(x2=1,diff(CDF2,x2)));
> IMT_g3:=1/evalf(subs(x3=1,diff(CDF3,x3)));
IMT_g1 := 3.0000000000000000000
IMT_g2 := 1.8472640247326625569
IMT_g3 := 3.3750000000000000001
> IMT_h1:=-evalf(subs(x1=1,diff(CDF1,x1$2)))/evalf(subs(x1=1,diff(CDF1,x
> 1)))^3;
> IMT_h2:=-evalf(subs(x2=1,diff(CDF2,x2$2)))/evalf(subs(x2=1,diff(CDF2,x
> 2)))^3;
> IMT_h3:=-evalf(subs(x3=1,diff(CDF3,x3$2)))/evalf(subs(x3=1,diff(CDF3,x
> 3)))^3;
IMT_h1 := -0.
IMT_h2 := 3.4123843770715149426
IMT_h3 := 17.085937500000000002
> diff(f(g(x)),x$2);
/ 2 \
(2) /d \2 |d |
(D )(f)(g(x)) |-- g(x)| + D(f)(g(x)) |--- g(x)|
\dx / | 2 |
\dx /
> IMT_h1*INEC_g1^2+IMT_g1*INEC_h1;
> IMT_h2*INEC_g2^2+IMT_g2*INEC_h2;
> IMT_h3*INEC_g3^2+IMT_g3*INEC_h3;
-0.46983704691100944408
0.34284791435655692599
-0.16736245021943200214
>
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