Fitting distribution to data

Extra Activity - 6

Introduction

Fitting a Distribution (Discrete)

Activity Overview:

This project applies key statistical analysis techniques using Python. The goal is to explore a dataset, fit a known distribution, and estimate its parameters using different methods.

Key Objectives:

Histogram for the Data: Visualize the distribution of the data to identify trends.
Fit a Known Distribution: Model the data using a Normal distribution.
Parameter Estimation: Calculate estimates using:
- Method of Moments (MoM)
- Maximum Likelihood Estimation (MLE)
Bootstrap Confidence Intervals: Form 95% confidence intervals using the bootstrap method to assess the accuracy of parameter estimates.

Dataset Description:

The Iris dataset contains 150 samples of iris flowers with measurements of sepal length, sepal width, petal length, and petal width across three species: Setosa, Versicolor, and Virginica.

Dataset :- Iris_Data

Iris

coolab Notebook

Google Colab

Statistical Analysis Results

Fitted Normal Distribution

The data was fitted using a Normal Distribution. The estimated parameters using two approaches are:

Method of Moments Estimates (MoM):
- Mean: 5.843
- Standard Deviation: 0.825
Maximum Likelihood Estimates (MLE):
- Mean: 5.843
- Standard Deviation: 0.825

Bootstrap Confidence Intervals

Using the Bootstrap Method (with 1000 resamples), approximate 95% confidence intervals were generated for both parameters.

Mean: [5.715, 5.969]
Standard Deviation: [0.760, 0.913]

Conclusion:

The Normal distribution provides a good fit for the Sepal Length data.
Both MoM and MLE gave consistent parameter estimates.
The confidence intervals indicate the level of uncertainty in the estimates, with a reasonably narrow range suggesting reliable results.

This comprehensive analysis highlights the effectiveness of using the Normal distribution for the given dataset.

Visualization

Summary

This project involved fitting a Normal distribution to the Sepal Length data from the Iris dataset using Python. The data was visualized using a histogram to observe its distribution. Parameter estimates were calculated using the Method of Moments (MoM) and Maximum Likelihood Estimation (MLE), both yielding a mean of 5.843 and a standard deviation of 0.825. Additionally, the Bootstrap method with 1000 resamples was used to generate 95% confidence intervals, resulting in a mean range of [5.715, 5.969] and a standard deviation range of [0.760, 0.913]. The analysis concluded that the Normal distribution provides a good fit for the data, with narrow confidence intervals indicating reliable parameter estimates.