Extra-Activity 5

In this project, we explore statistical data analysis by fitting a known probability distribution to the given dataset. We begin by visualizing the data through histograms and then apply statistical methods, including the method of moments and maximum likelihood estimation (MLE), to estimate the parameters of the selected distribution. Finally, we use the bootstrap method to construct approximate confidence intervals, highlighting the robustness and variability of our parameter estimates.

This approach not only emphasizes the theoretical aspects of parameter estimation but also demonstrates practical implementation using Python in a Google Colab environment.

Histogram for the Data: Visualize the data distribution using a histogram to identify patterns and potential distributions to fit.

Fit a Known Distribution: I have used Normal distribution to the data and estimated its parameters.

Method of Moments and Maximum Likelihood Estimates: Using google colab the method of moments and maximum likelihood estimates for the distribution's parameters has to be calculated.

Bootstrap Method for Confidence Intervals: Using the bootstrap method to generate approximate confidence intervals for the estimated parameters.

In this experiment, we analyzed a dataset by first visualizing its distribution using a histogram to understand the data’s structure. We then selected a known Normal distribution and fitted it to the data using the scipy.stats library. To estimate the parameters of the chosen distribution, we applied both the method of moments and maximum likelihood estimation techniques. Lastly, we used the bootstrap method to generate approximate confidence intervals for the parameters, ensuring robust statistical inference. This experiment demonstrates the use of various statistical techniques to fit distributions and estimate parameters effectively.