Show Non-Central T-Distribution in Statistics using Python

In the given problem statement we have to show the non-central T-distribution in statistics with the help of Python Programming. So to show this distribution we will use the python libraries.

The non-central T-distribution in statistics is a family of distribution which is shaped by degrees of freedom and non-centrality parameters. This distribution can be used in power analysis and hypothesis testing.

Understanding the Problem

The problem at hand is to show the non-central T-distribution using the Python libraries. So we will utilize the scipy.stats module. Because of this function we can show the distributions which also include non-central t-distribution. For defining the distribution we will use degrees of freedom and non centrality parameters.

Logic for The Above Problem

To solve the given problem we will import libraries like numpy, matplotlib and scipy.stats of Python. And also we will use degrees of freedom and non-centrality parameters.

Algorithm

• Step 1 − Import the necessary libraries like numpy, matplotlib and scipy.stats.

import numpy as nmp
import matplotlib.pyplot as plot
from scipy.stats import nct

• Step 2 − Now we will initiate the degree of freedom and non-centrality parameters as 'df' and 'nc'.

df = 10
nc = 2

• Step 3 − Next we will generate the values for x.

x = nmp.linspace(-5, 5, 500)

• Step 4 − Then we will calculate the PDF (Probability Density Function) of the non-central t-distribution.

pdf = nct.pdf(x, df, nc)

• Step 5 − At the end we will plot the PDF using matplotlib library. In our program we will use plot(), xlabel(), ylabel and title() functions. And to show the PDF we will use the show() method.

plot.plot(x, pdf)
plot.xlabel('x')
plot.ylabel('PDF')
plot.title('Non-Central T-Distribution')

# Show the distribution
plot.show()

Full Example

# Import the necessary libraries
import numpy as nmp
import matplotlib.pyplot as plot
from scipy.stats import nct

# Define the degree of freedom and non-centrality parameters
df = 10
nc = 2

# Generate the x values
x = nmp.linspace(-5, 5, 500)

# Probability density function
pdf = nct.pdf(x, df, nc)

# Plot the probability density function
plot.plot(x, pdf)
plot.xlabel('x')
plot.ylabel('PDF')
plot.title('Non-Central T-Distribution')

# Show the distribution
plot.show()

Output

Complexity

The time complexity for showing the non-central t-distribution in Python is O(N), here N is the number of x-values we have created in our program. So the time complexity for this code depends upon the x-values and probability density function calculation.

Conclusion

So we have successfully implemented the non-central t-distribution in Python using numpy, matplotlib and scipy libraries. We have generated the PDF using the scipy module in Python.