scipy stats.arcsine() | Python

The Arcsine distribution is a continuous probability distribution with a support on the interval [0, 1]. It is also called the arcsin distribution or the inverse sine distribution. It is a special case of the Beta distribution, which represents the distribution of probabilities, especially of a Binomial distribution, when it is assumed that the parameters are uniformly distributed between 0 and 1. It is often used in modeling a proportion, such as the proportion of a population that has some characteristic.

Syntax

scipy.stats.arcsine(loc=0, scale=1) 

• loc (optional): This parameter represents the starting point of the distribution, which corresponds to the minimum value of the interval. The default value is 0.
• scale (optional): This parameter represents the length of the interval, which corresponds to the maximum value of the interval minus the minimum value of the interval. The default value is 1.

Usage

The scipy.stats.arcsine() function returns a frozen Arcsine RV object, which can be used to generate random numbers from the Arcsine distribution or to calculate various statistical properties of the Arcsine distribution, such as the mean, variance, and skewness.

Example 1: Generate Random Numbers

from scipy.stats import arcsine
import matplotlib.pyplot as plt

rv = arcsine(loc=0, scale=1)
data = rv.rvs((1000,))
plt.hist(data, density=True, histtype='stepfilled', alpha=0.2)
plt.show()

This example generates 1000 random numbers from the Arcsine distribution with a starting point of 0 and a length of 1, and then plots a histogram of the generated data.

Example 2: Calculate Statistical Properties

from scipy.stats import arcsine

rv = arcsine(loc=0, scale=1)
mean, var, skew, kurt = rv.stats(moments='mvsk')
print('mean =', mean)
print('variance =', var)
print('skewness =', skew)
print('kurtosis =', kurt)

This example calculates the mean, variance, skewness, and kurtosis of the Arcsine distribution with a starting point of 0 and a length of 1.

Conclusion

The scipy.stats.arcsine() function is a useful tool for generating random numbers from the Arcsine distribution and calculating various statistical properties of the Arcsine distribution. It is particularly useful in modeling proportions and other quantities that are restricted to the interval [0, 1].