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
|
DOUBLE PRECISION FUNCTION dinvnr(p,q)
C**********************************************************************
C
C DOUBLE PRECISION FUNCTION DINVNR(P,Q)
C Double precision NoRmal distribution INVerse
C
C
C Function
C
C
C Returns X such that CUMNOR(X) = P, i.e., the integral from -
C infinity to X of (1/SQRT(2*PI)) EXP(-U*U/2) dU is P
C
C
C Arguments
C
C
C P --> The probability whose normal deviate is sought.
C P is DOUBLE PRECISION
C
C Q --> 1-P
C P is DOUBLE PRECISION
C
C
C Method
C
C
C The rational function on page 95 of Kennedy and Gentle,
C Statistical Computing, Marcel Dekker, NY , 1980 is used as a start
C value for the Newton method of finding roots.
C
C
C Note
C
C
C If P or Q .lt. machine EPS returns +/- DINVNR(EPS)
C
C**********************************************************************
C .. Parameters ..
INTEGER maxit
PARAMETER (maxit=100)
DOUBLE PRECISION eps
PARAMETER (eps=1.0D-13)
DOUBLE PRECISION r2pi
PARAMETER (r2pi=0.3989422804014326D0)
DOUBLE PRECISION nhalf
PARAMETER (nhalf=-0.5D0)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION p,q
C ..
C .. Local Scalars ..
DOUBLE PRECISION strtx,xcur,cum,ccum,pp,dx
INTEGER i
LOGICAL qporq
C ..
C .. External Functions ..
DOUBLE PRECISION stvaln
EXTERNAL stvaln
C ..
C .. External Subroutines ..
EXTERNAL cumnor
C ..
C .. Statement Functions ..
DOUBLE PRECISION dennor,x
dennor(x) = r2pi*exp(nhalf*x*x)
C ..
C .. Executable Statements ..
C
C FIND MINIMUM OF P AND Q
C
qporq = p .LE. q
IF (.NOT. (qporq)) GO TO 10
pp = p
GO TO 20
10 pp = q
C
C INITIALIZATION STEP
C
20 strtx = stvaln(pp)
xcur = strtx
C
C NEWTON INTERATIONS
C
DO 30,i = 1,maxit
CALL cumnor(xcur,cum,ccum)
dx = (cum-pp)/dennor(xcur)
xcur = xcur - dx
IF (abs(dx/xcur).LT.eps) GO TO 40
30 CONTINUE
dinvnr = strtx
C
C IF WE GET HERE, NEWTON HAS FAILED
C
IF (.NOT.qporq) dinvnr = -dinvnr
RETURN
C
C IF WE GET HERE, NEWTON HAS SUCCEDED
C
40 dinvnr = xcur
IF (.NOT.qporq) dinvnr = -dinvnr
RETURN
END
|
