Distributions

Some distributions

Triangular distribution

compmod.distributions.Triangular(mean=1.0, stdev=1.0)[source]

A triangular symetric distribution function that returns a frozen distribution of the scipy.stats.rv_continuous class.

Parameters:
  • mean (float) – mean value
  • stdev (float) – standard deviation
Return type:

scipy.stats.rv_continuous instance

 
>>> import compmod
>>> tri = compmod.distributions.Triangular
>>> tri = compmod.distributions.Triangular(mean = 1., stdev = .1)
>>> tri.rvs(10)
array([ 1.00410636,  1.05395898,  1.03192428,  1.01753651,  0.99951611,
        1.1718781 ,  0.94457269,  1.11406294,  1.08477038,  0.98861803])

import numpy as np
import matplotlib.pyplot as plt
from compmod.distributions import Triangular

N = 1000
mean, stdev = 5., 2.
tri = Triangular(mean = mean, stdev = stdev)
data = tri.rvs(N)

x =np.linspace(0., 10., 1000)
y = tri.pdf(x)
plt.figure()
plt.clf()
plt.hist(data, bins = int(N**.5), histtype='step', normed = True, label = "Generated Random Numbers")

plt.plot(x,y, "r-", label = "Probability Density Function")
plt.grid()
plt.legend(loc = "best")
plt.show()

(Source code, png, hires.png, pdf)

_images/triangular.png

Rectangular distribution

compmod.distributions.Rectangular(mean=1.0, stdev=1.0)[source]

A Rectangular symetric distribution function that returns a frozen uniforn distribution of the ‘scipy.stats.rv_continuous <http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.uniform.html>’_class.

param mean:mean value
type mean:float
param stdev:standard deviation
type stdev:float
rtype:scipy.stats.rv_continuous instance 
>>> import compmod 
>>> rec = compmod.distributions.Rectangular
>>> rec = compmod.distributions.Rectangular(mean = 5. , stdev = 2.) 
>>> rec.rvs(15)
array([ 6.30703805,  5.55772119,  5.69890282,  5.41807602,  6.78339394,
      1.83640732,  3.50697054,  7.97707174,  4.54666157,  7.27897515,
      2.33288284,  2.62291176,  1.80274279,  3.39480096,  6.09699301])

import numpy as np
import matplotlib.pyplot as plt
from compmod.distributions import Rectangular

N = 1000
mean, stdev = 2., 1./3.
rec = Rectangular(mean = mean, stdev = stdev)
data = rec.rvs(N)

x = np.linspace(0., 5., 1000)
y = rec.pdf(x)
plt.figure()
plt.clf()
plt.hist(data, bins = int(N**.5), histtype='step', normed = True, label = "Generated Random Numbers")

plt.plot(x,y, "r-", label = "Probability Density Function")
plt.grid()
plt.legend(loc = "best")
plt.show()

(Source code, png, hires.png, pdf)

_images/rectangular.png

Rayleigh distribution

compmod.distributions.Rayleigh(mean=1.0)[source]

A Rayleigh distribution function that returns a frozen distribution of the scipy.stats.rv_continuous class.

param mean:mean value
type mean:float
rtype:scipy.stats.rv_continuous instance 
>>> import compmod 
>>> ray = compmod.distributions.Rayleigh
>>> ray = compmod.distributions.Rayleigh(5.)
>>> ray.rvs(15)
array([ 4.46037568,  4.80288465,  5.37309281,  4.80523501,  5.39211872,
    4.50159587,  4.99945365,  4.96324001,  5.48935765,  6.3571905 ,
    5.01412849,  4.37768037,  5.99915989,  4.71909481,  5.25259294])

import numpy as np
import matplotlib.pyplot as plt
from compmod.distributions import Rayleigh
N = 1000
mean = 2
ray = Rayleigh(mean)
data = ray.rvs(N)
x =np.linspace(0., 10., 1000)
y = ray.pdf(x)
plt.figure()
plt.clf()
plt.hist(data, bins = int(N**.5), histtype='step', normed = True, label = "Generated Random Numbers")
plt.plot(x,y, "r-", label = "Probability Density Function")
plt.grid()
plt.legend(loc = "best")
plt.show()

(Source code, png, hires.png, pdf)

_images/rayleigh.png