diff options
Diffstat (limited to 'Lib/statistics.py')
| -rw-r--r-- | Lib/statistics.py | 155 |
1 files changed, 82 insertions, 73 deletions
diff --git a/Lib/statistics.py b/Lib/statistics.py index 77291dd6..c7d6568 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -824,6 +824,81 @@ def pstdev(data, mu=None): ## Normal Distribution ##################################################### + +def _normal_dist_inv_cdf(p, mu, sigma): + # 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: + r = 0.180625 - q * q + # Hash sum: 55.88319_28806_14901_4439 + num = (((((((2.50908_09287_30122_6727e+3 * r + + 3.34305_75583_58812_8105e+4) * r + + 6.72657_70927_00870_0853e+4) * r + + 4.59219_53931_54987_1457e+4) * r + + 1.37316_93765_50946_1125e+4) * r + + 1.97159_09503_06551_4427e+3) * r + + 1.33141_66789_17843_7745e+2) * r + + 3.38713_28727_96366_6080e+0) * q + den = (((((((5.22649_52788_52854_5610e+3 * r + + 2.87290_85735_72194_2674e+4) * r + + 3.93078_95800_09271_0610e+4) * r + + 2.12137_94301_58659_5867e+4) * r + + 5.39419_60214_24751_1077e+3) * r + + 6.87187_00749_20579_0830e+2) * r + + 4.23133_30701_60091_1252e+1) * r + + 1.0) + x = num / den + return mu + (x * sigma) + r = p if q <= 0.0 else 1.0 - p + r = sqrt(-log(r)) + if r <= 5.0: + r = r - 1.6 + # Hash sum: 49.33206_50330_16102_89036 + num = (((((((7.74545_01427_83414_07640e-4 * r + + 2.27238_44989_26918_45833e-2) * r + + 2.41780_72517_74506_11770e-1) * r + + 1.27045_82524_52368_38258e+0) * r + + 3.64784_83247_63204_60504e+0) * r + + 5.76949_72214_60691_40550e+0) * r + + 4.63033_78461_56545_29590e+0) * r + + 1.42343_71107_49683_57734e+0) + den = (((((((1.05075_00716_44416_84324e-9 * r + + 5.47593_80849_95344_94600e-4) * r + + 1.51986_66563_61645_71966e-2) * r + + 1.48103_97642_74800_74590e-1) * r + + 6.89767_33498_51000_04550e-1) * r + + 1.67638_48301_83803_84940e+0) * r + + 2.05319_16266_37758_82187e+0) * r + + 1.0) + else: + r = r - 5.0 + # Hash sum: 47.52583_31754_92896_71629 + num = (((((((2.01033_43992_92288_13265e-7 * r + + 2.71155_55687_43487_57815e-5) * r + + 1.24266_09473_88078_43860e-3) * r + + 2.65321_89526_57612_30930e-2) * r + + 2.96560_57182_85048_91230e-1) * r + + 1.78482_65399_17291_33580e+0) * r + + 5.46378_49111_64114_36990e+0) * r + + 6.65790_46435_01103_77720e+0) + den = (((((((2.04426_31033_89939_78564e-15 * r + + 1.42151_17583_16445_88870e-7) * r + + 1.84631_83175_10054_68180e-5) * r + + 7.86869_13114_56132_59100e-4) * r + + 1.48753_61290_85061_48525e-2) * r + + 1.36929_88092_27358_05310e-1) * r + + 5.99832_20655_58879_37690e-1) * r + + 1.0) + x = num / den + if q < 0.0: + x = -x + return mu + (x * sigma) + + class NormalDist: "Normal distribution of a random variable" # https://en.wikipedia.org/wiki/Normal_distribution @@ -882,79 +957,7 @@ class NormalDist: 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: - r = 0.180625 - q * q - # Hash sum: 55.88319_28806_14901_4439 - num = (((((((2.50908_09287_30122_6727e+3 * r + - 3.34305_75583_58812_8105e+4) * r + - 6.72657_70927_00870_0853e+4) * r + - 4.59219_53931_54987_1457e+4) * r + - 1.37316_93765_50946_1125e+4) * r + - 1.97159_09503_06551_4427e+3) * r + - 1.33141_66789_17843_7745e+2) * r + - 3.38713_28727_96366_6080e+0) * q - den = (((((((5.22649_52788_52854_5610e+3 * r + - 2.87290_85735_72194_2674e+4) * r + - 3.93078_95800_09271_0610e+4) * r + - 2.12137_94301_58659_5867e+4) * r + - 5.39419_60214_24751_1077e+3) * r + - 6.87187_00749_20579_0830e+2) * r + - 4.23133_30701_60091_1252e+1) * 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: - r = r - 1.6 - # Hash sum: 49.33206_50330_16102_89036 - num = (((((((7.74545_01427_83414_07640e-4 * r + - 2.27238_44989_26918_45833e-2) * r + - 2.41780_72517_74506_11770e-1) * r + - 1.27045_82524_52368_38258e+0) * r + - 3.64784_83247_63204_60504e+0) * r + - 5.76949_72214_60691_40550e+0) * r + - 4.63033_78461_56545_29590e+0) * r + - 1.42343_71107_49683_57734e+0) - den = (((((((1.05075_00716_44416_84324e-9 * r + - 5.47593_80849_95344_94600e-4) * r + - 1.51986_66563_61645_71966e-2) * r + - 1.48103_97642_74800_74590e-1) * r + - 6.89767_33498_51000_04550e-1) * r + - 1.67638_48301_83803_84940e+0) * r + - 2.05319_16266_37758_82187e+0) * r + - 1.0) - else: - r = r - 5.0 - # Hash sum: 47.52583_31754_92896_71629 - num = (((((((2.01033_43992_92288_13265e-7 * r + - 2.71155_55687_43487_57815e-5) * r + - 1.24266_09473_88078_43860e-3) * r + - 2.65321_89526_57612_30930e-2) * r + - 2.96560_57182_85048_91230e-1) * r + - 1.78482_65399_17291_33580e+0) * r + - 5.46378_49111_64114_36990e+0) * r + - 6.65790_46435_01103_77720e+0) - den = (((((((2.04426_31033_89939_78564e-15 * r + - 1.42151_17583_16445_88870e-7) * r + - 1.84631_83175_10054_68180e-5) * r + - 7.86869_13114_56132_59100e-4) * r + - 1.48753_61290_85061_48525e-2) * r + - 1.36929_88092_27358_05310e-1) * r + - 5.99832_20655_58879_37690e-1) * r + - 1.0) - x = num / den - if q < 0.0: - x = -x - return self._mu + (x * self._sigma) + return _normal_dist_inv_cdf(p, self._mu, self._sigma) def overlap(self, other): """Compute the overlapping coefficient (OVL) between two normal distributions. @@ -1078,6 +1081,12 @@ class NormalDist: def __repr__(self): return f'{type(self).__name__}(mu={self._mu!r}, sigma={self._sigma!r})' +# If available, use C implementation +try: + from _statistics import _normal_dist_inv_cdf +except ImportError: + pass + if __name__ == '__main__': |