Python – Pearson type-3 Distribution in Statistics
scipy.stats.pearson3() is a Pearson type III continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular distribution.
Parameters :
q : lower and upper tail probability
x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
size : [tuple of ints, optional] shape or random variates.
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).
Results : pearson type III continuous random variable
Code #1 : Creating pearson type III continuous random variable
from scipy.stats import pearson3
numargs = pearson3.numargs
a, b = 4.32 , 3.18
rv = pearson3(a, b)
print ( "RV : \n" , rv)
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Output :
RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6C55C48
Code #2 : pearson type III continuous variates and probability distribution
import numpy as np
quantile = np.arange ( 0.01 , 1 , 0.1 )
R = pearson3.rvs(a, b)
print ( "Random Variates : \n" , R)
R = pearson3.pdf(a, b, quantile)
print ( "\nProbability Distribution : \n" , R)
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Output :
Random Variates :
2.7215696051772347
Probability Distribution :
[0.00632525 0.00681964 0.00735457 0.00793359 0.00856061 0.00923989
0.00997614 0.01077451 0.01164069 0.01258094]
Code #3 : Graphical Representation.
import numpy as np
import matplotlib.pyplot as plt
distribution = np.linspace( 0 , np.minimum(rv.dist.b, 3 ))
print ( "Distribution : \n" , distribution)
plot = plt.plot(distribution, rv.pdf(distribution))
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Output :
Distribution :
[0. 0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
0.48979592 0.53061224 0.57142857 0.6122449 0.65306122 0.69387755
0.73469388 0.7755102 0.81632653 0.85714286 0.89795918 0.93877551
0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
1.2244898 1.26530612 1.30612245 1.34693878 1.3877551 1.42857143
1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
1.95918367 2. ]
Code #4 : Varying Positional Arguments
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace( 0 , 5 , 100 )
y1 = pearson3 .pdf(x, 1 , 3 , 5 )
y2 = pearson3 .pdf(x, 1 , 4 , 4 )
plt.plot(x, y1, "*" , x, y2, "r--" )
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Output :
Last Updated :
10 Jan, 2020
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