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Diffstat (limited to 'Lib/statistics.py')
| -rw-r--r-- | Lib/statistics.py | 95 |
1 files changed, 95 insertions, 0 deletions
diff --git a/Lib/statistics.py b/Lib/statistics.py index 8d79eed..fe68e58 100644 --- a/Lib/statistics.py +++ b/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. |