diff options
Diffstat (limited to 'Lib/statistics.py')
| -rw-r--r-- | Lib/statistics.py | 72 |
1 files changed, 38 insertions, 34 deletions
diff --git a/Lib/statistics.py b/Lib/statistics.py index f09f7be..ff07dc4 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -812,15 +812,15 @@ class NormalDist: # https://en.wikipedia.org/wiki/Normal_distribution # https://en.wikipedia.org/wiki/Variance#Properties - __slots__ = {'mu': 'Arithmetic mean of a normal distribution', - 'sigma': 'Standard deviation of a normal distribution'} + __slots__ = {'_mu': 'Arithmetic mean of a normal distribution', + '_sigma': 'Standard deviation of a normal distribution'} def __init__(self, mu=0.0, sigma=1.0): 'NormalDist where mu is the mean and sigma is the standard deviation.' if sigma < 0.0: raise StatisticsError('sigma must be non-negative') - self.mu = mu - self.sigma = sigma + self._mu = mu + self._sigma = sigma @classmethod def from_samples(cls, data): @@ -833,21 +833,21 @@ class NormalDist: def samples(self, n, *, seed=None): 'Generate *n* samples for a given mean and standard deviation.' gauss = random.gauss if seed is None else random.Random(seed).gauss - mu, sigma = self.mu, self.sigma + mu, sigma = self._mu, self._sigma return [gauss(mu, sigma) for i in range(n)] def pdf(self, x): 'Probability density function. P(x <= X < x+dx) / dx' - variance = self.sigma ** 2.0 + variance = self._sigma ** 2.0 if not variance: raise StatisticsError('pdf() not defined when sigma is zero') - return exp((x - self.mu)**2.0 / (-2.0*variance)) / sqrt(tau * variance) + return exp((x - self._mu)**2.0 / (-2.0*variance)) / sqrt(tau * variance) def cdf(self, x): 'Cumulative distribution function. P(X <= x)' - if not self.sigma: + if not self._sigma: raise StatisticsError('cdf() not defined when sigma is zero') - return 0.5 * (1.0 + erf((x - self.mu) / (self.sigma * sqrt(2.0)))) + 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 @@ -859,7 +859,7 @@ class NormalDist: ''' 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: + 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 @@ -888,7 +888,7 @@ class NormalDist: 4.23133_30701_60091_1252e+1) * r + 1.0) x = num / den - return self.mu + (x * self.sigma) + return self._mu + (x * self._sigma) r = p if q <= 0.0 else 1.0 - p r = sqrt(-log(r)) if r <= 5.0: @@ -930,7 +930,7 @@ class NormalDist: x = num / den if q < 0.0: x = -x - return self.mu + (x * self.sigma) + return self._mu + (x * self._sigma) def overlap(self, other): '''Compute the overlapping coefficient (OVL) between two normal distributions. @@ -951,17 +951,17 @@ class NormalDist: if not isinstance(other, NormalDist): raise TypeError('Expected another NormalDist instance') X, Y = self, other - if (Y.sigma, Y.mu) < (X.sigma, X.mu): # sort to assure commutativity + if (Y._sigma, Y._mu) < (X._sigma, X._mu): # sort to assure commutativity X, Y = Y, X X_var, Y_var = X.variance, Y.variance if not X_var or not Y_var: raise StatisticsError('overlap() not defined when sigma is zero') dv = Y_var - X_var - dm = fabs(Y.mu - X.mu) + dm = fabs(Y._mu - X._mu) if not dv: - return 1.0 - erf(dm / (2.0 * X.sigma * sqrt(2.0))) - a = X.mu * Y_var - Y.mu * X_var - b = X.sigma * Y.sigma * sqrt(dm**2.0 + dv * log(Y_var / X_var)) + return 1.0 - erf(dm / (2.0 * X._sigma * sqrt(2.0))) + a = X._mu * Y_var - Y._mu * X_var + b = X._sigma * Y._sigma * sqrt(dm**2.0 + dv * log(Y_var / X_var)) x1 = (a + b) / dv x2 = (a - b) / dv return 1.0 - (fabs(Y.cdf(x1) - X.cdf(x1)) + fabs(Y.cdf(x2) - X.cdf(x2))) @@ -969,17 +969,17 @@ class NormalDist: @property def mean(self): 'Arithmetic mean of the normal distribution.' - return self.mu + return self._mu @property def stdev(self): 'Standard deviation of the normal distribution.' - return self.sigma + return self._sigma @property def variance(self): 'Square of the standard deviation.' - return self.sigma ** 2.0 + return self._sigma ** 2.0 def __add__(x1, x2): '''Add a constant or another NormalDist instance. @@ -992,8 +992,8 @@ class NormalDist: independent or if they are jointly normally distributed. ''' if isinstance(x2, NormalDist): - return NormalDist(x1.mu + x2.mu, hypot(x1.sigma, x2.sigma)) - return NormalDist(x1.mu + x2, x1.sigma) + return NormalDist(x1._mu + x2._mu, hypot(x1._sigma, x2._sigma)) + return NormalDist(x1._mu + x2, x1._sigma) def __sub__(x1, x2): '''Subtract a constant or another NormalDist instance. @@ -1006,8 +1006,8 @@ class NormalDist: independent or if they are jointly normally distributed. ''' if isinstance(x2, NormalDist): - return NormalDist(x1.mu - x2.mu, hypot(x1.sigma, x2.sigma)) - return NormalDist(x1.mu - x2, x1.sigma) + return NormalDist(x1._mu - x2._mu, hypot(x1._sigma, x2._sigma)) + return NormalDist(x1._mu - x2, x1._sigma) def __mul__(x1, x2): '''Multiply both mu and sigma by a constant. @@ -1015,7 +1015,7 @@ class NormalDist: Used for rescaling, perhaps to change measurement units. Sigma is scaled with the absolute value of the constant. ''' - return NormalDist(x1.mu * x2, x1.sigma * fabs(x2)) + return NormalDist(x1._mu * x2, x1._sigma * fabs(x2)) def __truediv__(x1, x2): '''Divide both mu and sigma by a constant. @@ -1023,15 +1023,15 @@ class NormalDist: Used for rescaling, perhaps to change measurement units. Sigma is scaled with the absolute value of the constant. ''' - return NormalDist(x1.mu / x2, x1.sigma / fabs(x2)) + return NormalDist(x1._mu / x2, x1._sigma / fabs(x2)) def __pos__(x1): 'Return a copy of the instance.' - return NormalDist(x1.mu, x1.sigma) + return NormalDist(x1._mu, x1._sigma) def __neg__(x1): 'Negates mu while keeping sigma the same.' - return NormalDist(-x1.mu, x1.sigma) + return NormalDist(-x1._mu, x1._sigma) __radd__ = __add__ @@ -1045,10 +1045,14 @@ class NormalDist: 'Two NormalDist objects are equal if their mu and sigma are both equal.' if not isinstance(x2, NormalDist): return NotImplemented - return (x1.mu, x2.sigma) == (x2.mu, x2.sigma) + return (x1._mu, x2._sigma) == (x2._mu, x2._sigma) + + def __hash__(self): + 'NormalDist objects hash equal if their mu and sigma are both equal.' + return hash((self._mu, self._sigma)) def __repr__(self): - return f'{type(self).__name__}(mu={self.mu!r}, sigma={self.sigma!r})' + return f'{type(self).__name__}(mu={self._mu!r}, sigma={self._sigma!r})' if __name__ == '__main__': @@ -1065,8 +1069,8 @@ if __name__ == '__main__': g2 = NormalDist(-5, 25) # Test scaling by a constant - assert (g1 * 5 / 5).mu == g1.mu - assert (g1 * 5 / 5).sigma == g1.sigma + assert (g1 * 5 / 5).mean == g1.mean + assert (g1 * 5 / 5).stdev == g1.stdev n = 100_000 G1 = g1.samples(n) @@ -1090,8 +1094,8 @@ if __name__ == '__main__': print(NormalDist.from_samples(map(func, repeat(const), G1))) def assert_close(G1, G2): - assert isclose(G1.mu, G1.mu, rel_tol=0.01), (G1, G2) - assert isclose(G1.sigma, G2.sigma, rel_tol=0.01), (G1, G2) + assert isclose(G1.mean, G1.mean, rel_tol=0.01), (G1, G2) + assert isclose(G1.stdev, G2.stdev, rel_tol=0.01), (G1, G2) X = NormalDist(-105, 73) Y = NormalDist(31, 47) |