[PYTHON] Write a kernel density function

1 What you want to do

Generate a kernel density function with Jupyter and visualize it. Click here for a description of the kernel density function [https://www.ie-kau.net/entry/kernel_density_est)

2 code

The kernel density function seems to have a slightly different shape depending on whether the gaussian_kde function is used or the seabon kdeplot function is used.

/home/sampletest/sample.py

from numpy.random import randn
import seaborn as sns
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde
sns.set_style("whitegrid")
from scipy.integrate import cumtrapz #Library for integrating pdf in all intervals



#Give a dataset and generate a kernel density function. It also calculates the cumulative frequency of the kernel density function and
#Cumulative value down,Returns the X value that is up.

def pdf_kernel(dataset,down,up):

    d_max=np.max(dataset)+0.2
    d_min=np.min(dataset)-0.2

    d_kernel = gaussian_kde(dataset) #Generate a kernel density estimation function. Bandwidth is calculated automatically.

    #Specify the range to be integrated: d_min to d_Integrate in the range of max.
    d_xs = np.linspace(d_min, d_max, num=1000)

    #Kernel density function input(d_xs)And output(d_ys)Is defined.
    d_ys = d_kernel(d_xs)

    #Cumulative distribution function d_Integrate in the range of xs.
    d_integral = cumtrapz(d_ys, d_xs)

    #cdf(x) = 0.Find x that is 03. d_0 in the integral array.The number closest to 03 is calculated as the number in the array.
    idx_d= np.searchsorted(d_integral, down)

    #cdf(x) = 0.Find x that is 9. d_0 in the integral array.The number closest to 9 is calculated as the number in the array.
    idx_u = np.searchsorted(d_integral, up)


    #The graph is displayed.
    ax=plt.plot(d_xs, d_ys, label="KDE")
    plt.xlim(d_min-1, d_max+1) 

    #Cumulative value 5%Show range of
    plt.fill_between(d_xs[:idx_d], 0, d_ys[:idx_d], facecolor="r", alpha=0.5)


    #Cumulative value 90%Show range of
    plt.fill_between(d_xs[idx_u:], 0, d_ys[idx_u:], facecolor="r", alpha=0.5)

    #Legend displayed in the upper right
    plt.legend(loc="upper right")

    pdf_val={"down":d_xs[idx_d],"up":d_xs[idx_u]}
    return pdf_val



#The main program starts from the following
dataset = randn(50) #Generate 50 random numbers that follow a uniform distribution
down=0.05 
up=0.9


#Give a dataset and generate a kernel density function. It also calculates the cumulative frequency of the kernel density function and
#Cumulative value down,Returns the X value that is up.
val=pdf_kernel(dataset,down,up) 

#Write a kernel density function using seaborn.
sns.kdeplot(dataset,label="from seaborn")

Execution result </ b> #The range of cumulative value 0 to down (5% in the illustrated example) and the range of cumulative value up (90% in the illustrated example) to 100% are displayed.