diff options
Diffstat (limited to 'Lib/statistics.py')
| -rw-r--r-- | Lib/statistics.py | 34 |
1 files changed, 23 insertions, 11 deletions
diff --git a/Lib/statistics.py b/Lib/statistics.py index 58fb31def88..fc00891b083 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -919,13 +919,13 @@ def kde(data, h, kernel='normal', *, cumulative=False): sqrt2pi = sqrt(2 * pi) sqrt2 = sqrt(2) K = lambda t: exp(-1/2 * t * t) / sqrt2pi - I = lambda t: 1/2 * (1.0 + erf(t / sqrt2)) + W = lambda t: 1/2 * (1.0 + erf(t / sqrt2)) support = None case 'logistic': # 1.0 / (exp(t) + 2.0 + exp(-t)) K = lambda t: 1/2 / (1.0 + cosh(t)) - I = lambda t: 1.0 - 1.0 / (exp(t) + 1.0) + W = lambda t: 1.0 - 1.0 / (exp(t) + 1.0) support = None case 'sigmoid': @@ -933,39 +933,39 @@ def kde(data, h, kernel='normal', *, cumulative=False): c1 = 1 / pi c2 = 2 / pi K = lambda t: c1 / cosh(t) - I = lambda t: c2 * atan(exp(t)) + W = lambda t: c2 * atan(exp(t)) support = None case 'rectangular' | 'uniform': K = lambda t: 1/2 - I = lambda t: 1/2 * t + 1/2 + W = lambda t: 1/2 * t + 1/2 support = 1.0 case 'triangular': K = lambda t: 1.0 - abs(t) - I = lambda t: t*t * (1/2 if t < 0.0 else -1/2) + t + 1/2 + W = lambda t: t*t * (1/2 if t < 0.0 else -1/2) + t + 1/2 support = 1.0 case 'parabolic' | 'epanechnikov': K = lambda t: 3/4 * (1.0 - t * t) - I = lambda t: -1/4 * t**3 + 3/4 * t + 1/2 + W = lambda t: -1/4 * t**3 + 3/4 * t + 1/2 support = 1.0 case 'quartic' | 'biweight': K = lambda t: 15/16 * (1.0 - t * t) ** 2 - I = lambda t: 3/16 * t**5 - 5/8 * t**3 + 15/16 * t + 1/2 + W = lambda t: 3/16 * t**5 - 5/8 * t**3 + 15/16 * t + 1/2 support = 1.0 case 'triweight': K = lambda t: 35/32 * (1.0 - t * t) ** 3 - I = lambda t: 35/32 * (-1/7*t**7 + 3/5*t**5 - t**3 + t) + 1/2 + W = lambda t: 35/32 * (-1/7*t**7 + 3/5*t**5 - t**3 + t) + 1/2 support = 1.0 case 'cosine': c1 = pi / 4 c2 = pi / 2 K = lambda t: c1 * cos(c2 * t) - I = lambda t: 1/2 * sin(c2 * t) + 1/2 + W = lambda t: 1/2 * sin(c2 * t) + 1/2 support = 1.0 case _: @@ -974,10 +974,14 @@ def kde(data, h, kernel='normal', *, cumulative=False): if support is None: def pdf(x): + n = len(data) return sum(K((x - x_i) / h) for x_i in data) / (n * h) def cdf(x): - return sum(I((x - x_i) / h) for x_i in data) / n + + n = len(data) + return sum(W((x - x_i) / h) for x_i in data) / n + else: @@ -985,16 +989,24 @@ def kde(data, h, kernel='normal', *, cumulative=False): bandwidth = h * support def pdf(x): + nonlocal n, sample + if len(data) != n: + sample = sorted(data) + n = len(data) i = bisect_left(sample, x - bandwidth) j = bisect_right(sample, x + bandwidth) supported = sample[i : j] return sum(K((x - x_i) / h) for x_i in supported) / (n * h) def cdf(x): + nonlocal n, sample + if len(data) != n: + sample = sorted(data) + n = len(data) i = bisect_left(sample, x - bandwidth) j = bisect_right(sample, x + bandwidth) supported = sample[i : j] - return sum((I((x - x_i) / h) for x_i in supported), i) / n + return sum((W((x - x_i) / h) for x_i in supported), i) / n if cumulative: cdf.__doc__ = f'CDF estimate with {h=!r} and {kernel=!r}' |