I am trying to model a Levy walk using scipy.stats.levy
. It works fine except for the fact that there are a few steps which are VERY large and I would like to know if there is a proper way to limit the stepsize.
Here is the code I am using:
import numpy as np
from scipy.stats import uniform
from scipy.stats import levy
import matplotlib.pyplot as plt
def levy_walk( n ):
# uniformly distributed angles
angle = uniform.rvs( size=(n,), loc=.0, scale=2.*np.pi )
# levy distributed step length
r = levy.rvs( size=n )
# x and y coordinates (position added to previous coordinate --> cum. sum)
x = np.cumsum( r * np.cos(angle) )
y = np.cumsum( r * np.sin(angle) )
return np.array( (x, y, r, angle) )
# number of steps to simulate
n = 500
# get levy walk (strictly speaking, it seems to be a flight)
foo = levy_walk( n )
# initialize figure
fig = plt.figure( figsize=(14,6) )
# plot 2D random walk with Levy stepsize
ax1 = fig.add_subplot( 1,2,1 )
ax1.plot( foo[0,:], foo[1,:] )
ax1.set_xlabel( 'x' )
ax1.set_ylabel( 'y' )
ax1.set_title( '2D Levy flight' )
# plot histogram
ax2 = fig.add_subplot( 1,2,2 )
num_bins = n/10
ax2.hist( foo[2,:], bins=n/10 )
ax2.set_yscale( 'log' )
ax2.set_xlabel( 'stepsize' )
ax2.set_title( 'histogram' )
plt.show()
And this is an example output figure where you can clearly see the occurrence of very few but VERY large steps:
So, my question is what is the proper way to limit the step size ? (Using the scale
option does not really help as it only scales everything down)
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