sympy.stats.ExGaussian() in python

With the help of sympy.stats.ExGaussian() method, we can get the continuous random variable representing the exponentially modified gaussian distribution.

Syntax : sympy.stats.ExGaussian(name, mean, std, rate)
Return : Return continuous random variable.

Example #1 :
In this example we can see that by using sympy.stats.ExGaussian() method, we are able to get the continuous random variable which represents the Exponentially modified Gaussian distribution by using this method.

# Import sympy and ExGaussian
from sympy.stats import ExGaussian, density
from sympy import Symbol

mean = Symbol("mean", integer = True, positive = True)
std = Symbol("std", integer = True, positive = True)
rate = Symbol("rate", integer = True, positive = True)
z = Symbol("z")

# Using sympy.stats.ExGaussian() method
X = ExGaussian("x", mean, std, rate)
gfg = density(X)(z)

pprint(gfg)

Output :

/ 2 \
rate*\2*mean + rate*std – 2*z/
——————————- / ___ / 2 \\
2 |\/ 2 *\mean + rate*std – z/|
rate*e *erfc|—————————-|
\ 2*std /
————————————————————————
2

Example #2 :

# Import sympy and ExGaussian
from sympy.stats import ExGaussian, density
from sympy import Symbol

mean = 22
std = 21
rate = 7
z = 0.4

# Using sympy.stats.ExGaussian() method
X = ExGaussian("x", mean, std, rate)
gfg = density(X)(z)

pprint(gfg)

Output :

/ ___\
3.50044639861837e+4758*erfc\74.0142857142857*\/ 2 /