bell Namespace Reference

How to Make a Bell Curve in Python? More...

Functions
def	pdf (x)
	A custom function to calculate the probability distribution function. More...
def	plot (x, xlabel="", ylabel="")
	Plot the curve by using matplotlib. More...
def	plot2 (x, title="")
	Plot the curve by using seaborn. More...
def	plot3 (x, title="", xlabel="", ylabel="", fig=None, ax=None)
	Plot the histogram by using matplotlib. More...
def	showPlot (show=True, file_name="bell.png")
	Draw the graphics. More...
def	main (argv=None)
	Main program for plotting the curve. More...

Detailed Description

How to Make a Bell Curve in Python?

A bell-shaped curve in statistics corresponds to a normal distribution or a Gaussian distribution which has been named after German mathematician Carl Friedrich Gauss.
In a normal distribution, the points are concentrated on the mean values and most of the points lie near the mean.

The orientation of the bell-curve depends on the mean and standard deviation values of a given set of input points.
By changing the value of the mean we can shift the location of the curve on the axis and the shape of the curve can be manipulated by changing the standard deviation values.

In a normal distribution, mean, median, and mode are all equal and the bell-shaped curve is symmetric about the mean i.e., the y-axis.

The probability density function for a normal distribution is calculated using the formula:

\(f(x,\mu,\sigma) = {{1} \over {\sigma \sqrt{2\pi}}} \exp^{{{-1} \over{2}} \times {\left({{x-\mu} \over {\sigma}}\right)}^{2}},\ -\infty < x < \infty\)

• f(x) is the probability density function.
• μ is the mean.
• σ is the standard deviation.

Packages required: macOS:

• py310-numpy
• py310-matplotlib

Ubuntu:

• python3-numpy
• python3-matplotlib

Author

Paulo Roma

Since

24/03/2022

See also

https://www.geeksforgeeks.org/how-to-make-a-bell-curve-in-python/

https://www.statology.org/bell-curve-google-sheets/

https://trumpexcel.com/bell-curve/

https://www.automateexcel.com/charts/bell-curve-plot-template/

Function Documentation

main()

def bell.main

(

argv = None

)

Main program for plotting the curve.

Parameters

argv	commnad line arguments. argv[0]: script path. argv[1]: number of random values.

References plot(), plot2(), and showPlot().

pdf()

def bell.pdf

(

x

)

A custom function to calculate the probability distribution function.

Parameters

x	list of values.

Returns

function to calculate the y coordinate for each x in the list of values.

Referenced by plot().

plot()

def bell.plot	(		x,
			xlabel = "",
			ylabel = ""
	)

Plot the curve by using matplotlib.

Parameters

x	list of values.
xlabel	x axis label.
ylabel	y axis label.

See also

https://matplotlib.org/3.5.1/api/_as_gen/matplotlib.pyplot.plot.html

https://matplotlib.org/3.5.1/api/_as_gen/matplotlib.pyplot.scatter.html

https://numpy.org/doc/stable/reference/generated/numpy.sort.html

References pdf().

Referenced by main(), and data.main().

plot2()

def bell.plot2	(		x,
			title = ""
	)

Plot the curve by using seaborn.

Parameters

x	list of values (pandas.DataFrame, numpy.ndarray, mapping, or sequence).
title	curve title.

See also

https://seaborn.pydata.org/generated/seaborn.histplot.html

https://seaborn.pydata.org/generated/seaborn.boxplot.html

https://seaborn.pydata.org/generated/seaborn.distplot.html

Referenced by main(), and data.main().

plot3()

def bell.plot3	(		x,
			title = "",
			xlabel = "",
			ylabel = "",
			fig = None,
			ax = None
	)

Plot the histogram by using matplotlib.

Parameters

x	list of values.
title	curve title.
xlabel	x axis label.
ylabel	y axis label.
fig	figure containing subplots.
ax	axis for drawing.

See also

https://matplotlib.org/3.5.1/api/_as_gen/matplotlib.pyplot.hist.html

Referenced by data.main().

showPlot()

def bell.showPlot	(		show = True,
			file_name = "bell.png"
	)

Draw the graphics.

Parameters

show	whether draw or save the graphics.
file_name	name of the file to save the figure.

See also

https://matplotlib.org/3.5.1/api/_as_gen/matplotlib.pyplot.show.html

https://matplotlib.org/3.5.1/api/figure_api.html#matplotlib.figure.Figure.savefig

Referenced by main(), and data.main().