copuladensity-pkg 0.0.1

A package for calculate and draw copula density

Package info

Package name: copuladensity-pkg
Version: 0.0.1
Author: Shanshan Wang
Description: this package is used to calcualte and draw copula density of two correlated time series.

Python requires version >=3.6

Install

pip install copuladensity-pkg

Uninstall

pip uninstall copuladensity-pkg

How to use

from copula_package import copula_density

Functions

• copula_density.sampling_two_corr_time_series(mean,cov,n)
  function: sample two correlated time series
  mean: a list of two mean values for two time series, respectively, e.g., mean = (1, 2)
  cov: a 2-d array of diagonal covariances between two time series, e.g., cov = [[1, 1], [1, 2]]
  n: the length of each time series
  return x, y, z
  x: a list of time series
  y: a list of time series
  z: a pandas dataframe for x and y
  
  
• copula_density.draw_histogram(x,n_bins,label_x)
  function: draw historgram of a time series, where the hight of histogram shows the probability density
  x: a list of time series
  n_bins: the number of bins in the histogram
  label_x: a string for the label of x axis in the figure
  return: none
  
  
• copula_density.draw_joint_distribution(z,label_x,label_y)
  function: draw joint distribution of two time series z: a pandas dataframe with two columns, where each column contains a time series
  label_x: a string for the label of x axis in the figure
  label_y: a string for the label of y axis in the figure
  return: none
  
  
• copula_density.qrank_data(x)
  function: calculate the quantile of ranking data x
  x: a list of time series
  return: qx
  qx: a list of quantiles
  
  
• copula_density.calc_copula_density(qx,qy,nx,ny)
  function: calculate copula density of two time series
  qx: a list of quantiles
  qy: a list of quantiles
  nx: the number of bins for qx
  nx: the number of bins for qy
  return: cop_den
  cop_den: a $nx\times ny$ 2-dimentional array of copula densities
  
  
• copula_density.draw_heatmap(matrix,label_qx,label_qy)
  function: draw heatmap for copula densities
  matrix: 2-dimensional array of copula densities
  label_x: a string for the label of x axis in the figure
  label_y: a string for the label of y axis in the figure
  return: none
  
  
• copula_density.draw_surface(matrix,label_qx,label_qy)
  function: draw surface for copula densities
  matrix: 2-dimensional array of copula densities
  label_x: a string for the label of x axis in the figure
  label_y: a string for the label of y axis in the figure
  return: none
  
  
• copula_density.draw_bar3d(matrix,label_qx,label_qy)
  function: draw 3-dimensional bars for copula densities
  matrix: 2-dimensional array of copula densities
  label_x: a string for the label of x axis in the figure
  label_y: a string for the label of y axis in the figure
  return: none
  
  

An example

from copula_package import copula_density 

# sampling two time series
mean = (1, 2)
cov = [[1, 1], [1, 2]]
n=10000
x,y,z=copula_density.sampling_two_corr_time_series(mean,cov,n) 

# draw histogram and joint histogram of time series
n_bins=50
label_x='x'
label_y='y'
copula_density.draw_histogram(x,n_bins,label_x)
copula_density.draw_joint_distribution(z,label_x,label_y)

# calculate quantiles
qx=copula_density.qrank_data(x)
qy=copula_density.qrank_data(y)

# calcualte copula density
nx=20
ny=20
cop_den=copula_density.calc_copula_density(qx,qy,nx,ny)

# draw copula density in three ways
label_qx='Quantile(x)'
label_qy='Quantitle(y)'
copula_density.draw_heatmap(cop_den,label_qx,label_qy)
copula_density.draw_surface(cop_den,label_qx,label_qy)
copula_density.draw_bar3d(cop_den,label_qx,label_qy)