stat_utils

#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Sat Mar  2 22:17:24 2019

@author: xies
"""
import numpy as np
import matplotlib.pyplot as plt

def plot_ci_manual(t, s_err, n, x, x2, y2, ax=None):
    """Return an axes of confidence bands using a simple approach.

    Notes
    -----
    .. math:: \left| \: \hat{\mu}_{y|x0} - \mu_{y|x0} \: \right| \; \leq \; T_{n-2}^{.975} \; \hat{\sigma} \; \sqrt{\frac{1}{n}+\frac{(x_0-\bar{x})^2}{\sum_{i=1}^n{(x_i-\bar{x})^2}}}
    .. math:: \hat{\sigma} = \sqrt{\sum_{i=1}^n{\frac{(y_i-\hat{y})^2}{n-2}}}

    References
    ----------
    .. [1]: M. Duarte.  "Curve fitting," JUpyter Notebook.
       http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/CurveFitting.ipynb

    """
    if ax is None:
        ax = plt.gca()

    ci = t*s_err*np.sqrt(1/n + (x2-np.mean(x))**2/np.sum((x-np.mean(x))**2))
    ax.fill_between(x2, y2+ci, y2-ci, color="#b9cfe7", edgecolor="")

    return ax