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MATH05, Non parametric tests

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Non parametric

from scipy import stats
from scipy import optimize
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(style="whitegrid")

X = stats.chi2(df=5) 
X_samples = X.rvs(100)

kde = stats.kde.gaussian_kde(X_samples)
kde_low_bw = stats.kde.gaussian_kde(X_samples, bw_method=0.25)

x = np.linspace(0, 20, 100)

fig, axes = plt.subplots(1, 3, figsize=(12, 3)) 
axes[0].hist(X_samples, normed=True, alpha=0.5, bins=25)   
axes[1].plot(x, kde(x), label="KDE")   
axes[1].plot(x, kde_low_bw(x), label="KDE (low bw)")   
axes[1].plot(x, X.pdf(x), label="True PDF")  
axes[1].legend()   
sns.distplot(X_samples, bins=25, ax=axes[2])

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additional kde 
kde.resample(10)

array([[ 2.21027713,  2.86300834,  5.63643055,  9.93925447, 11.0112984 ,
         5.53754038,  4.57539167,  0.18351943,  5.84327588,  5.67924786]])



def _kde_cdf(x): 
    return kde.integrate_box_1d(-np.inf, x)

def _kde_ppf(q):
    return optimize.fsolve(lambda x, q: kde_cdf(x) - q, kde. dataset.mean(), args=(q,))[0] 
    
kde_cdf = np.vectorize(_kde_cdf)
kde_ppf = np.vectorize(_kde_ppf)
kde_ppf([0.05, 0.95])

array([0.53427617, 8.06347491])

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