bigau-probability 3.1

Gaussian and Binomial distributions

bigau_probability

Gaussian and Binomial Distributions

This package contains code for some basic Gaussian and Binomial distribitions. For Gaussian distribution, you can calculate the mean and standard deviation from a sample input file. You can plot histograms from data and probability density functions (PDF). You can calculate PDF for a point, add two gaussian instances and print a description for a gaussian instance.

Installation

pip install bigau-probability

Gaussian Distribution Methods

Import

Before using the gaussian methods defined in this package, you have to import the Gaussian class

from bigau_probability import Gaussian

Instantiating Gaussian

A Gaussian object can be instantiated by passing in the mean and standard deviation parameters.Alternatively, it can be instantiated without parameters for example in the case that data is in another file. See examples below

gaussian1 = Gaussian(5, 10)  # creates a gaussian distribution with mean of 5 and stdev of 10
gaussian2 = Gaussian() # creates a gaussian distribution with no parameters

Reading Data File

The read_data_file method is used for reading data from a file. This becomes very handy when you have quite a number of data to process. The expected data content are usually numbers, one per line. A sample data file is shown below
1
3
99
100
120
32
330
23
76
44
31

The read_data_file method takes in a parameter, the name of the file containing data. Be sure to put the file in the same directory you are running your code from. Suppose the data above is stored in a .txt file called gaussian.txt, you would call the read_data_file method as shown below:

gaussian2.read_data_file('gaussian.txt')

Calculating mean

The calculate_mean method is used to calculate the mean of a gaussian distribution. It returns the mean of the distribution.

gaussian2.calculate_mean()

Calculating standard deviation

The calculate_stdev() method is used to calculate the standard deviation of a gaussian distribution. It returns the standard deviation of the distribution.

gaussian2.calculate_stdev()

Calculating probability density function

The pdf method is used for calculate the probability density function of a given value x. It takes a parameter x which is a number as input. It returns the probability density function of x.

gaussian2.pdf(50)

Plotting histogram

The plot_histogram method is used to display a histogram of the gaussian distribution. It uses mathplotlib for the plot.

gaussian2.plot_histogram()

Plotting histogram for probability distribution function

The plot_histogram_pdf is used plot the normalized histogram of the data and a plot of the probability density function along the same range. It optional takes an integer that specifies the number of data points. If no parameter is passed, it uses a default value of 50. This method returns the x and y axis of the histogram besides showing the plot.

gaussian2.plot_histogram_pdf()

Adding two gaussian distributions

You can add two gaussian distributions by using the addition symbol (+). This will show the mean and standard deviation of the resultant gaussian distribution.

gaussian1 + gaussian2

Printing a gaussian object

The print method displays the mean and the standard deviation of a given gaussian distribution

print(gaussian1)

Binomial Distribution Methods

Import

Before using the binomial methods defined in this package, you have to import the Binomial class

from bigau_probability import Binomial

Instantiating Binomial

A Binomial object can be instantiated without parameters for example in the case that data is in another file. See examples below

binomial = Binomial()  # creates a binomial distribution with no parameters

Reading Data File

The read_data_file method is used for reading data from a file. The expected data content are usually trial outcomes, one per line. For example, the tossing of a coin 13 times may have outcomes like the sample data shown below with 1 representing a head and 0 representing a tail.

0
1
1
1
1
1
0
1
0
1
0
1
0

The read_data_file method takes in a parameter, the name of the file containing data. Be sure to put the file in the same directory you are running your code from. Suppose the data above is stored in a .txt file called binomial.txt, you would call the read_data_file method as shown below:

binomial.read_data_file('binomial.txt')

Generating stats from data

The replace_stats_with_data method is used to generate the probability and sample size from a given binomial data. It is recommended to call this method immediately a data file is read.

binomial.replace_stats_with_data()

Calculating mean

The calculate_mean method is used to calculate the mean of a binomial distribution. It returns the mean of the distribution.

binomial.calculate_mean()

Calculating standard deviation

The calculate_stdev() method is used to calculate the standard deviation of a binomial distribution. It returns the standard deviation of the distribution.

binomial.calculate_stdev()

Plotting Barchart

The plot_bar method is used to display a barchar of the binomial distribution. It uses mathplotlib for the plot.

binomial.plot_bar()

Plotting Barchart for probability distribution function

The plot_bar_pdf method is used to plot a bar chart for the probability density function from k = 0 to k = n This method returns the x and y axis of the barchart besides showing the plot.

binomial.plot_bar_pdf()

Adding two binomial distributions

You can add two binomial distributions by using the addition symbol (+). This will show the mean, standard deviation, probability and sample size of the resultant gaussian distribution.

binomial + binomial

Printing a gaussian object

The print method displays the mean, standard deviation, probability and sample size of a given binomial distribution

print(binomial)

Source Code

https://github.com/grace-omotoso/Bigau_Probability