/// <summary>
        /// Quantile function (Inverse CDF) for the normal distribution.
        /// </summary>
        /// <param name="p">Probability.</param>
        /// <param name="mu">Mean of normal distribution.</param>
        /// <param name="sigma">Standard deviation of normal distribution.</param>
        /// <param name="lower_tail">If true, probability is P[X <= x], otherwise P[X > x].</param>
        /// <param name="log_p">If true, probabilities are given as log(p).</param>
        /// <returns>P[X <= x] where x ~ N(mu,sigma^2)</returns>
        /// <remarks>See https://svn.r-project.org/R/trunk/src/nmath/qnorm.c</remarks>
        private double Quantile(double p, double mu, double sigma, bool lower_tail, bool log_p)
        {
            if (double.IsNaN(p) || double.IsNaN(mu) || double.IsNaN(sigma))
                return Double.NaN;
            double ans;
            bool isBoundaryCase = R_Q_P01_boundaries(p, double.NegativeInfinity, double.PositiveInfinity, lower_tail, log_p, out ans);
            if (isBoundaryCase) return (ans);
            if (sigma < 0) return (double.NaN);
            if (sigma == 0) return (mu);

            double p_ = R_DT_qIv(p, lower_tail, log_p);
            double q = p_ - 0.5;
            double r, val;

            if (Math.Abs(q) <= 0.425)  // 0.075 <= p <= 0.925
            {
                r = .180625 - q * q;
                val = q * (((((((r * 2509.0809287301226727 +
                           33430.575583588128105) * r + 67265.770927008700853) * r +
                         45921.953931549871457) * r + 13731.693765509461125) * r +
                       1971.5909503065514427) * r + 133.14166789178437745) * r +
                     3.387132872796366608)
                / (((((((r * 5226.495278852854561 +
                         28729.085735721942674) * r + 39307.89580009271061) * r +
                       21213.794301586595867) * r + 5394.1960214247511077) * r +
                     687.1870074920579083) * r + 42.313330701600911252) * r + 1.0);
            }
            else
            {
                r = q > 0 ? R_DT_CIv(p, lower_tail, log_p) : p_;
                r = Math.Sqrt(-((log_p && ((lower_tail && q <= 0) || (!lower_tail && q > 0))) ? p : Math.Log(r)));

                if (r <= 5)              // <==> min(p,1-p) >= exp(-25) ~= 1.3888e-11
                {
                    r -= 1.6;
                    val = (((((((r * 7.7454501427834140764e-4 +
                            .0227238449892691845833) * r + .24178072517745061177) *
                          r + 1.27045825245236838258) * r +
                         3.64784832476320460504) * r + 5.7694972214606914055) *
                       r + 4.6303378461565452959) * r +
                      1.42343711074968357734)
                     / (((((((r *
                              1.05075007164441684324e-9 + 5.475938084995344946e-4) *
                             r + .0151986665636164571966) * r +
                            .14810397642748007459) * r + .68976733498510000455) *
                          r + 1.6763848301838038494) * r +
                         2.05319162663775882187) * r + 1.0);
                }
                else                     // very close to  0 or 1
                {
                    r -= 5.0;
                    val = (((((((r * 2.01033439929228813265e-7 +
                            2.71155556874348757815e-5) * r +
                           .0012426609473880784386) * r + .026532189526576123093) *
                         r + .29656057182850489123) * r +
                        1.7848265399172913358) * r + 5.4637849111641143699) *
                      r + 6.6579046435011037772)
                     / (((((((r *
                              2.04426310338993978564e-15 + 1.4215117583164458887e-7) *
                             r + 1.8463183175100546818e-5) * r +
                            7.868691311456132591e-4) * r + .0148753612908506148525)
                          * r + .13692988092273580531) * r +
                         .59983220655588793769) * r + 1.0);
                }
                if (q < 0.0) val = -val;
            }

            return (mu + sigma * val);
        }