平方误差和（SSE）的分布拟合
这是Saullo答案的更新和修改，它使用当前scipy.stats分布的完整列表，并返回分布的直方图和数据的直方图之间SSE最小的分布。
拟合示例
使用中的ElNiño数据集statsmodels进行拟合，并确定误差。返回错误最少的分布。
所有发行
最佳拟合分布
范例程式码
%matplotlib inline
import warnings
import numpy as np
import pandas as pd
import scipy.stats as st
import statsmodels as sm
import matplotlib
import matplotlib.pyplot as plt
matplotlib.rcParams['figure.figsize'] = (16.0, 12.0)
matplotlib.style.use('ggplot')
# Create models from data
def best_fit_distribution(data, bins=200, ax=None):
"""Model data by finding best fit distribution to data"""
# Get histogram of original data
y, x = np.histogram(data, bins=bins, density=True)
x = (x + np.roll(x, -1))[:-1] / 2.0
# Distributions to check
DISTRIBUTIONS = [
st.alpha,st.anglit,st.arcsine,st.beta,st.betaprime,st.bradford,st.burr,st.cauchy,st.chi,st.chi2,st.cosine,
st.dgamma,st.dweibull,st.erlang,st.expon,st.exponnorm,st.exponweib,st.exponpow,st.f,st.fatiguelife,st.fisk,
st.foldcauchy,st.foldnorm,st.frechet_r,st.frechet_l,st.genlogistic,st.genpareto,st.gennorm,st.genexpon,
st.genextreme,st.gausshyper,st.gamma,st.gengamma,st.genhalflogistic,st.gilbrat,st.gompertz,st.gumbel_r,
st.gumbel_l,st.halfcauchy,st.halflogistic,st.halfnorm,st.halfgennorm,st.hypsecant,st.invgamma,st.invgauss,
st.invweibull,st.johnsonsb,st.johnsonsu,st.ksone,st.kstwobign,st.laplace,st.levy,st.levy_l,st.levy_stable,
st.logistic,st.loggamma,st.loglaplace,st.lognorm,st.lomax,st.maxwell,st.mielke,st.nakagami,st.ncx2,st.ncf,
st.nct,st.norm,st.pareto,st.pearson3,st.powerlaw,st.powerlognorm,st.powernorm,st.rdist,st.reciprocal,
st.rayleigh,st.rice,st.recipinvgauss,st.semicircular,st.t,st.triang,st.truncexpon,st.truncnorm,st.tukeylambda,
st.uniform,st.vonmises,st.vonmises_line,st.wald,st.weibull_min,st.weibull_max,st.wrapcauchy
]
# Best holders
best_distribution = st.norm
best_params = (0.0, 1.0)
best_sse = np.inf
# Estimate distribution parameters from data
for distribution in DISTRIBUTIONS:
# Try to fit the distribution
try:
# Ignore warnings from data that can't be fit
with warnings.catch_warnings():
warnings.filterwarnings('ignore')
# fit dist to data
params = distribution.fit(data)
# Separate parts of parameters
arg = params[:-2]
loc = params[-2]
scale = params[-1]
# Calculate fitted PDF and error with fit in distribution
pdf = distribution.pdf(x, loc=loc, scale=scale, *arg)
sse = np.sum(np.power(y - pdf, 2.0))
# if axis pass in add to plot
try:
if ax:
pd.Series(pdf, x).plot(ax=ax)
end
except Exception:
pass
# identify if this distribution is better
if best_sse > sse > 0:
best_distribution = distribution
best_params = params
best_sse = sse
except Exception:
pass
return (best_distribution.name, best_params)
def make_pdf(dist, params, size=10000):
"""Generate distributions's Probability Distribution Function """
# Separate parts of parameters
arg = params[:-2]
loc = params[-2]
scale = params[-1]
# Get sane start and end points of distribution
start = dist.ppf(0.01, *arg, loc=loc, scale=scale) if arg else dist.ppf(0.01, loc=loc, scale=scale)
end = dist.ppf(0.99, *arg, loc=loc, scale=scale) if arg else dist.ppf(0.99, loc=loc, scale=scale)
# Build PDF and turn into pandas Series
x = np.linspace(start, end, size)
y = dist.pdf(x, loc=loc, scale=scale, *arg)
pdf = pd.Series(y, x)
return pdf
# Load data from statsmodels datasets
data = pd.Series(sm.datasets.elnino.load_pandas().data.set_index('YEAR').values.ravel())
# Plot for comparison
plt.figure(figsize=(12,8))
ax = data.plot(kind='hist', bins=50, normed=True, alpha=0.5, color=plt.rcParams['axes.color_cycle'][1])
# Save plot limits
dataYLim = ax.get_ylim()
# Find best fit distribution
best_fit_name, best_fit_params = best_fit_distribution(data, 200, ax)
best_dist = getattr(st, best_fit_name)
# Update plots
ax.set_ylim(dataYLim)
ax.set_title(u'El Niño sea temp.\n All Fitted Distributions')
ax.set_xlabel(u'Temp (°C)')
ax.set_ylabel('Frequency')
# Make PDF with best params
pdf = make_pdf(best_dist, best_fit_params)
# Display
plt.figure(figsize=(12,8))
ax = pdf.plot(lw=2, label='PDF', legend=True)
data.plot(kind='hist', bins=50, normed=True, alpha=0.5, label='Data', legend=True, ax=ax)
param_names = (best_dist.shapes + ', loc, scale').split(', ') if best_dist.shapes else ['loc', 'scale']
param_str = ', '.join(['{}={:0.2f}'.format(k,v) for k,v in zip(param_names, best_fit_params)])
dist_str = '{}({})'.format(best_fit_name, param_str)
ax.set_title(u'El Niño sea temp. with best fit distribution \n' + dist_str)
ax.set_xlabel(u'Temp. (°C)')
ax.set_ylabel('Frequency')
