#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""Visualize the percentile function of the t_k distribution."""

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats


def g(k, alphas):
    """Calculate the percentile values of a t_k distribution."""
    # Create a variable representing the distribution
    rv = scipy.stats.t(k)

    values = [rv.ppf(alpha) for alpha in alphas]
    return values


def main(xmin=0.01, xmax=0.99, samples=200):
    """Create plot."""
    font = {'size': 20}
    plt.rc('font', **font)

    alphas = np.linspace(xmin, xmax, samples)
    for k, color in [(1, '#000000'), (2, '#ff0000'), (5, '#00ff00')]:
        plt.plot(alphas, g(k, alphas),
                 color=color,
                 label=r"$t_%i(\alpha)$" % k)
    plt.title(u"Quantile function of $t_k$")
    plt.xlabel(r"""$\alpha$""")
    plt.ylabel(r"""$t_{k;\alpha}$""")
    plt.legend()
    # plt.show()
    plt.savefig("t-k-quantile-function.svg")


if __name__ == '__main__':
    main()