bpo-36324: Add inv_cdf() to statistics.NormalDist() (GH-12377)

Lib/statistics.py

@@ -745,6 +745,101 @@ class NormalDist:
             raise StatisticsError('cdf() not defined when sigma is zero')
         return 0.5 * (1.0 + erf((x - self.mu) / (self.sigma * sqrt(2.0))))
 
+    def inv_cdf(self, p):
+        ''' Inverse cumulative distribution function:  x : P(X <= x) = p
+
+         Finds the value of the random variable such that the probability of the
+         variable being less than or equal to that value equals the given probability.
+
+         This function is also called the percent-point function or quantile function.
+
+        '''
+        if (p <= 0.0 or p >= 1.0):
+            raise StatisticsError('p must be in the range 0.0 < p < 1.0')
+        if self.sigma <= 0.0:
+            raise StatisticsError('cdf() not defined when sigma at or below zero')
+
+        # There is no closed-form solution to the inverse CDF for the normal
+        # distribution, so we use a rational approximation instead:
+        # Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
+        # Normal Distribution".  Applied Statistics. Blackwell Publishing. 37
+        # (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
+
+        q = p - 0.5
+        if fabs(q) <= 0.425:
+            a0 = 3.38713_28727_96366_6080e+0
+            a1 = 1.33141_66789_17843_7745e+2
+            a2 = 1.97159_09503_06551_4427e+3
+            a3 = 1.37316_93765_50946_1125e+4
+            a4 = 4.59219_53931_54987_1457e+4
+            a5 = 6.72657_70927_00870_0853e+4
+            a6 = 3.34305_75583_58812_8105e+4
+            a7 = 2.50908_09287_30122_6727e+3
+            b1 = 4.23133_30701_60091_1252e+1
+            b2 = 6.87187_00749_20579_0830e+2
+            b3 = 5.39419_60214_24751_1077e+3
+            b4 = 2.12137_94301_58659_5867e+4
+            b5 = 3.93078_95800_09271_0610e+4
+            b6 = 2.87290_85735_72194_2674e+4
+            b7 = 5.22649_52788_52854_5610e+3
+            r = 0.180625 - q * q
+            num = (q * (((((((a7 * r + a6) * r + a5) * r + a4) * r + a3)
+                        * r + a2) * r + a1) * r + a0))
+            den = ((((((((b7 * r + b6) * r + b5) * r + b4) * r + b3)
+                        * r + b2) * r + b1) * r + 1.0))
+            x = num / den
+            return self.mu + (x * self.sigma)
+
+        r = p if q <= 0.0 else 1.0 - p
+        r = sqrt(-log(r))
+        if r <= 5.0:
+            c0 = 1.42343_71107_49683_57734e+0
+            c1 = 4.63033_78461_56545_29590e+0
+            c2 = 5.76949_72214_60691_40550e+0
+            c3 = 3.64784_83247_63204_60504e+0
+            c4 = 1.27045_82524_52368_38258e+0
+            c5 = 2.41780_72517_74506_11770e-1
+            c6 = 2.27238_44989_26918_45833e-2
+            c7 = 7.74545_01427_83414_07640e-4
+            d1 = 2.05319_16266_37758_82187e+0
+            d2 = 1.67638_48301_83803_84940e+0
+            d3 = 6.89767_33498_51000_04550e-1
+            d4 = 1.48103_97642_74800_74590e-1
+            d5 = 1.51986_66563_61645_71966e-2
+            d6 = 5.47593_80849_95344_94600e-4
+            d7 = 1.05075_00716_44416_84324e-9
+            r = r - 1.6
+            num = ((((((((c7 * r + c6) * r + c5) * r + c4) * r + c3)
+                      * r + c2) * r + c1) * r + c0))
+            den = ((((((((d7 * r + d6) * r + d5) * r + d4) * r + d3)
+                      * r + d2) * r + d1) * r + 1.0))
+        else:
+            e0 = 6.65790_46435_01103_77720e+0
+            e1 = 5.46378_49111_64114_36990e+0
+            e2 = 1.78482_65399_17291_33580e+0
+            e3 = 2.96560_57182_85048_91230e-1
+            e4 = 2.65321_89526_57612_30930e-2
+            e5 = 1.24266_09473_88078_43860e-3
+            e6 = 2.71155_55687_43487_57815e-5
+            e7 = 2.01033_43992_92288_13265e-7
+            f1 = 5.99832_20655_58879_37690e-1
+            f2 = 1.36929_88092_27358_05310e-1
+            f3 = 1.48753_61290_85061_48525e-2
+            f4 = 7.86869_13114_56132_59100e-4
+            f5 = 1.84631_83175_10054_68180e-5
+            f6 = 1.42151_17583_16445_88870e-7
+            f7 = 2.04426_31033_89939_78564e-15
+            r = r - 5.0
+            num = ((((((((e7 * r + e6) * r + e5) * r + e4) * r + e3)
+                      * r + e2) * r + e1) * r + e0))
+            den = ((((((((f7 * r + f6) * r + f5) * r + f4) * r + f3)
+                      * r + f2) * r + f1) * r + 1.0))
+
+        x = num / den
+        if q < 0.0:
+            x = -x
+        return self.mu + (x * self.sigma)
+
     def overlap(self, other):
         '''Compute the overlapping coefficient (OVL) between two normal distributions.