"""
Some common distributions are defined in this module. That way, users can easily build
more complicated expressions without making them look hard.
I have deliberately chosen to start these function with a capital, e.g.
Gaussian instead of gaussian, because this makes the resulting expressions more
readable.
"""
import sympy
[docs]def Gaussian(x, mu, sig):
"""
Gaussian pdf.
:param x: free variable.
:param mu: mean of the distribution.
:param sig: standard deviation of the distribution.
:return: sympy.Expr for a Gaussian pdf.
"""
return sympy.exp(-(x - mu)**2/(2*sig**2))/sympy.sqrt(2*sympy.pi*sig**2)
[docs]def Exp(x, l):
"""
Exponential Distribution pdf.
:param x: free variable.
:param l: rate parameter.
:return: sympy.Expr for an Exponential Distribution pdf.
"""
return l * sympy.exp(- l * x)
# def Beta():
# sympy.stats.Beta()