diff --git a/Lib/statistics.py b/Lib/statistics.py index f193fcdc241..e2b59267f04 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -248,6 +248,7 @@ def geometric_mean(data): found_zero = True else: raise StatisticsError('No negative inputs allowed', x) + total = fsum(map(log, count_positive(data))) if not n: @@ -710,6 +711,7 @@ def correlation(x, y, /, *, method='linear'): start = (n - 1) / -2 # Center rankings around zero x = _rank(x, start=start) y = _rank(y, start=start) + else: xbar = fsum(x) / n ybar = fsum(y) / n @@ -1213,91 +1215,6 @@ def quantiles(data, *, n=4, method='exclusive'): ## 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) - - -# If available, use C implementation -try: - from _statistics import _normal_dist_inv_cdf -except ImportError: - pass - - class NormalDist: "Normal distribution of a random variable" # https://en.wikipedia.org/wiki/Normal_distribution @@ -1561,11 +1478,13 @@ def _sum(data): types_add = types.add partials = {} partials_get = partials.get + for typ, values in groupby(data, type): types_add(typ) for n, d in map(_exact_ratio, values): count += 1 partials[d] = partials_get(d, 0) + n + if None in partials: # The sum will be a NAN or INF. We can ignore all the finite # partials, and just look at this special one. @@ -1574,6 +1493,7 @@ def _sum(data): else: # Sum all the partial sums using builtin sum. total = sum(Fraction(n, d) for d, n in partials.items()) + T = reduce(_coerce, types, int) # or raise TypeError return (T, total, count) @@ -1596,6 +1516,7 @@ def _ss(data, c=None): types_add = types.add sx_partials = defaultdict(int) sxx_partials = defaultdict(int) + for typ, values in groupby(data, type): types_add(typ) for n, d in map(_exact_ratio, values): @@ -1605,11 +1526,13 @@ def _ss(data, c=None): if not count: ssd = c = Fraction(0) + elif None in sx_partials: # The sum will be a NAN or INF. We can ignore all the finite # partials, and just look at this special one. ssd = c = sx_partials[None] assert not _isfinite(ssd) + else: sx = sum(Fraction(n, d) for d, n in sx_partials.items()) sxx = sum(Fraction(n, d*d) for d, n in sxx_partials.items()) @@ -1693,8 +1616,10 @@ def _convert(value, T): # This covers the cases where T is Fraction, or where value is # a NAN or INF (Decimal or float). return value + if issubclass(T, int) and value.denominator != 1: T = float + try: # FIXME: what do we do if this overflows? return T(value) @@ -1857,3 +1782,88 @@ def _sqrtprod(x: float, y: float) -> float: # https://www.wolframalpha.com/input/?i=Maclaurin+series+sqrt%28h**2+%2B+x%29+at+x%3D0 d = sumprod((x, h), (y, -h)) return h + d / (2.0 * h) + + +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) + + +# If available, use C implementation +try: + from _statistics import _normal_dist_inv_cdf +except ImportError: + pass