Extra Activity 5 Stats II

Things to do in this activity is 

1. Histogram for the data.

2. Fit one of the known distributions to the data.

3. Calculate method of moments estimate and ML estimate for the unknown parameter(s) of the selected distribution.

4. Use the bootstrap method to form approximate confidence intervals for the parameters, if applicable.

    We have used Google Colab to perform Monte Carlo simulation

1.  To open the Google sheet file Click here

2.  To open the Google Colab file Click here

Conclusion

In this notebook, we analyzed a dataset by following a series of key steps to better understand the underlying distribution and estimate its parameters. Here's a brief overview of the steps completed and their results:

1. Histogram of the Data: We began by visualizing the distribution of the data using a histogram. The histogram provided an initial impression of the data's shape and helped us hypothesize the type of distribution that might best fit the data.

2. Fitting a Known Distribution: Based on the shape of the histogram, we selected an appropriate probability distribution to fit to the data (e.g., Normal, Exponential, Poisson, etc.). The fitting process involved estimating the parameters of the distribution using methods such as Maximum Likelihood Estimation (MLE).

3. Method of Moments and Maximum Likelihood Estimates: We then computed the parameter estimates using two common statistical methods:

   • Method of Moments (MME): This approach estimates the parameters by equating sample moments (mean, variance, etc.) with the corresponding moments of the chosen theoretical distribution.

   • Maximum Likelihood Estimation (MLE): MLE is a method that finds the parameter values that maximize the likelihood function given the observed data. Both MME and MLE estimates were calculated and compared to assess their accuracy.

4. Bootstrap Confidence Intervals: To quantify the uncertainty around the parameter estimates, we employed the bootstrap method. By resampling the data and recalculating the estimates repeatedly, we obtained empirical confidence intervals for the parameters. This provided a robust way to evaluate the precision of the estimated parameters.