Introduction to sympy.stats.LogLogistic()

Sympy.stats.LogLogistic() is a statistical distribution in the SymPy library of Python. It represents the log-logistic distribution which is a continuous probability distribution. The log-logistic distribution is characterized by two parameters, scale and shape.

from sympy.stats import LogLogistic, density, cdf
from sympy import symbols

x, s, a = symbols('x s a')
distribution = LogLogistic('x', s, a)

The LogLogistic() function takes three parameters: the variable of the distribution, the scale parameter s, and the shape parameter a. The variable is normally denoted by x.

The density() function can be used to calculate the probability density function for a given value of x.

density(distribution)(x)

The cdf() function can be used to calculate the cumulative distribution function for a given value of x.

cdf(distribution)(x)

You can also generate random samples from the LogLogistic distribution using the .sample() method.

samples = distribution.sample(5)

In conclusion, sympy.stats.LogLogistic() is a useful tool for probability and statistics computations in Python, especially when working with log-logistic distributions. It provides a convenient way to calculate the probability density and cumulative distribution functions, as well as generate random samples from the distribution.