Comparing the quality of the two confidence interval types of: * Asymptotic Confidence Interval * Log Likelihood Ratio Confidence Interval Uses a hands-on demonstration through a Lindley Distribution. The Lindely distribution is a weighted mixture distribution using both gamma and exponential components. Its shape most likely does not fully fit either distribution type in its best form, but explanation and analysis can describe either the asymptotic CI or log likelihood CI as the stronger confidence interval for the Lindley Distribution. Confidence Intervals are used as a measurement for the possible range of values the parameter is expected to take on.

Finding Comparative estimators through method of moments (MME), Maximum Likelihood Function (MLE) and Hessian Matrix.

Details the Maximum Likelihood Estimation (MLE) characteristics and details strengths and weaknesses. The MLE is compared to Method of Moment Estimation (MME) in function and characterizing the data set.

Active demonstration of methods of moment estimation using a log-logistic distribution. Using a distribution to estimate parameters of a distribution via computational methods and making comparisons with distribution bootstrapping resampling.

Detailed description of the difference of Asymptotic Sampling Distributions and Bootstrap Sampling with paired simulation and data set examples.

Homework two: An analysis of the relationships and connections between normal, t, chi-squared, and F distributions.

Estimating CDF and PDF using computation R functions. Based on datasets in failure times to generate an Empirical Cumulative Distribution Function.