1 #ifndef STAN_MATH_PRIM_SCAL_FUN_INV_PHI_HPP
2 #define STAN_MATH_PRIM_SCAL_FUN_INV_PHI_HPP
27 stan::math::check_bounded<double, double, double>(
"inv_Phi",
28 "Probability variable", p, 0, 1);
35 static const double a[6] = {
36 -3.969683028665376e+01, 2.209460984245205e+02,
37 -2.759285104469687e+02, 1.383577518672690e+02,
38 -3.066479806614716e+01, 2.506628277459239e+00
40 static const double b[5] = {
41 -5.447609879822406e+01, 1.615858368580409e+02,
42 -1.556989798598866e+02, 6.680131188771972e+01,
43 -1.328068155288572e+01
45 static const double c[6] = {
46 -7.784894002430293e-03, -3.223964580411365e-01,
47 -2.400758277161838e+00, -2.549732539343734e+00,
48 4.374664141464968e+00, 2.938163982698783e+00
50 static const double d[4] = {
51 7.784695709041462e-03, 3.224671290700398e-01,
52 2.445134137142996e+00, 3.754408661907416e+00
55 static const double p_low = 0.02425;
56 static const double p_high = 0.97575;
59 if ((p_low <= p) && (p <= p_high)) {
62 x = (((((a[0]*r + a[1])*r + a[2])*r + a[3])*r + a[4])*r + a[5])*q
63 / (((((b[0]*r + b[1])*r + b[2])*r + b[3])*r + b[4])*r + 1.0);
64 }
else if (p < p_low) {
66 x = (((((c[0]*q + c[1])*q + c[2])*q + c[3])*q + c[4])*q + c[5])
67 / ((((d[0]*q + d[1])*q + d[2])*q + d[3])*q + 1.0);
70 x = -(((((c[0]*q + c[1])*q + c[2])*q + c[3])*q + c[4])*q + c[5])
71 / ((((d[0]*q + d[1])*q + d[2])*q + d[3])*q + 1.0);
77 x -= u / (1.0 + 0.5 * x * u);
fvar< T > sqrt(const fvar< T > &x)
fvar< T > inv_Phi(const fvar< T > &p)
fvar< T > log(const fvar< T > &x)
const double SQRT_2_TIMES_SQRT_PI
fvar< T > exp(const fvar< T > &x)
fvar< T > Phi(const fvar< T > &x)
double e()
Return the base of the natural logarithm.
const double INFTY
Positive infinity.
const double NEGATIVE_INFTY
Negative infinity.
fvar< T > log1m(const fvar< T > &x)