import marimo

__generated_with = "0.25.1"
app = marimo.App()


@app.cell
def _():
    import marimo as mo

    return (mo,)


@app.cell(hide_code=True)
def _(mo):
    mo.md(r"""
    # "Student" t-distribution

    Visit [Wikipedia](https://en.wikipedia.org/wiki/Student%27s_t-distribution) for a quick review. The name is because of  the developer, William Sealy Gosset, who worked for Guinness and published under the pseudonym "Student".
    """)
    return


@app.cell
def _():
    # Author: Jake VanderPlas
    # License: BSD
    #   The figure produced by this code is published in the textbook
    #   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
    #   For more information, see http://astroML.github.com
    #   To report a bug or issue, use the following forum:
    #    https://groups.google.com/forum/#!forum/astroml-general
    import numpy as np
    from scipy.stats import t as student_t
    from matplotlib import pyplot as plt

    plt.rcParams['figure.figsize'] = 12, 10 
    plt.rcParams['font.size'] = 16 

    #----------------------------------------------------------------------
    # This function adjusts matplotlib settings for a uniform feel in the textbook.
    # Note that with usetex=True, fonts are rendered with LaTeX.  This may
    # result in an error if LaTeX is not installed on your system.  In that case,
    # you can set usetex to False.
    # from astroML.plotting import setup_text_plots
    # setup_text_plots(fontsize=8, usetex=True)

    #------------------------------------------------------------
    # Define the distribution parameters to be plotted
    mu = 0
    k_values = [1E10, 2, 1, 0.5]
    linestyles = ['-', '--', ':', '-.']
    x = np.linspace(-10, 10, 1000)

    #------------------------------------------------------------
    # plot the distributions
    fig, ax = plt.subplots(figsize=(5, 3.75))

    for k, ls in zip(k_values, linestyles):
        dist = student_t(k, 0)

        if k >= 1E10:
            label = r'$\mathrm{t}(k=\infty)$'
        else:
            label = r'$\mathrm{t}(k=%.1f)$' % k

        plt.plot(x, dist.pdf(x), ls=ls, c='black', label=label)

    plt.xlim(-5, 5)
    plt.ylim(0.0, 0.45)

    plt.xlabel('$x$')
    plt.ylabel(r'$p(x|k)$')
    plt.title("Student's $t$ Distribution")

    plt.legend(bbox_to_anchor=(1.25, 1.0))
    plt.show()
    return np, student_t


@app.cell
def _():
    ## Lets do an example, thanks to Prof. Cimbala
    return


@app.cell
def _():
    from IPython.display import YouTubeVideo
    # a talk about IPython at Sage Days at U. Washington, Seattle.
    # Video credit: William Stein.
    YouTubeVideo('pVk3w9aaSSo')
    return


@app.cell
def _():
    # measured quantities:
    x_mean = 8.24  # kOhm
    Sx = 0.314  # kOhm
    N = 20  # samples
    _confidence_level = 0.95
    # for the 95 confidence level
    alpha = 1 - _confidence_level  # 95%
    degrees_of_freedom = N - 1
    return N, Sx, alpha, degrees_of_freedom, x_mean


@app.cell
def _():
    # how to get values from the distribution? try to google it down:
    # http://stackoverflow.com/questions/27315161/displaying-a-youtube-clip-in-python
    return


@app.cell
def _(alpha, degrees_of_freedom, student_t):
    #Student, n=999, p<0.05, 2-tail
    #equivalent to Excel TINV(0.05,999)
    print('Two tail problem:'); 
    print(student_t.ppf(1-alpha/2.0, degrees_of_freedom))
    t_value = student_t.ppf(1-alpha/2.0, degrees_of_freedom)

    #Student, n=999, p<0.05%, Single tail
    #equivalent to Excel TINV(2*0.05,999)
    print('Single tail:')
    print(student_t.ppf(1-alpha, degrees_of_freedom))
    return (t_value,)


@app.cell
def _(N, Sx, np, t_value, x_mean):
    # the answer: 
    # the population mean is 

    print('Population mean is :')
    print('{:.3f} +- {:.3f}'.format(x_mean, t_value*Sx/(np.sqrt(N))))
    return


@app.cell
def _(N, Sx, degrees_of_freedom, np, student_t, x_mean):
    _confidence_level = 0.99
    alpha_1 = 1 - _confidence_level
    t_value_1 = student_t.ppf(1 - alpha_1 / 2.0, degrees_of_freedom)
    print('t-value is higher {:.3f}'.format(t_value_1))
    print('Population mean is :')
    print('{:.3f} +- {:.3f}'.format(x_mean, t_value_1 * Sx / np.sqrt(N)))
    return


if __name__ == "__main__":
    app.run()