latex_normal_distribution.py

A plot of the Normal (Gaussian) distribution. his example demonstrates the use of mathtext on axes and in Div objects.

Details

Bokeh APIs

Figure.line, Figure.quad, bokeh.models.Div, bokeh.models.TeX

More info

Styling visual attributes > Adding mathematical notations

Keywords

mathtext, latex

import numpy as np

from bokeh.layouts import column
from bokeh.models import Div, TeX
from bokeh.plotting import figure, show

p = figure(width=670, height=400, toolbar_location=None,
           title="Normal (Gaussian) Distribution")

n = 1000
rng = np.random.default_rng(825914)
x = rng.normal(loc=4.7, scale=12.3, size=n)

# Scale random data so that it has mean of 0 and standard deviation of 1
xbar = x.mean()
sigma = x.std()
scaled = (x - xbar) / sigma

# Histogram
bins = np.linspace(-3, 3, 40)
hist, edges = np.histogram(scaled, density=True, bins=bins)
p.quad(top=hist, bottom=0, left=edges[:-1], right=edges[1:],
         fill_color="skyblue", line_color="white",
         legend_label=f"{n} random samples")

# Probability density function
x = np.linspace(-3.0, 3.0, 100)
pdf = np.exp(-0.5*x**2) / np.sqrt(2.0*np.pi)
p.line(x, pdf, line_width=2, line_color="navy",
       legend_label="Probability Density Function")

p.y_range.start = 0
p.xaxis.axis_label = "x"
p.yaxis.axis_label = "PDF(x)"

p.xaxis.ticker = [-3, -2, -1, 0, 1, 2, 3]
p.xaxis.major_label_overrides = {
    -3: TeX(r"\overline{x} - 3\sigma"),
    -2: TeX(r"\overline{x} - 2\sigma"),
    -1: TeX(r"\overline{x} - \sigma"),
     0: TeX(r"\overline{x}"),
     1: TeX(r"\overline{x} + \sigma"),
     2: TeX(r"\overline{x} + 2\sigma"),
     3: TeX(r"\overline{x} + 3\sigma"),
}

p.yaxis.ticker = [0, 0.1, 0.2, 0.3, 0.4]
p.yaxis.major_label_overrides = {
    0: TeX(r"0"),
    0.1: TeX(r"0.1/\sigma"),
    0.2: TeX(r"0.2/\sigma"),
    0.3: TeX(r"0.3/\sigma"),
    0.4: TeX(r"0.4/\sigma"),
}

div = Div(text=r"""
A histogram of a samples from a Normal (Gaussian) distribution, together with
the ideal probability density function, given by the equation:
<p />
$$
\qquad PDF(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left[-\frac{1}{2}
\left(\frac{x-\overline{x}}{\sigma}\right)^2 \right]
$$
""")

show(column(p, div))