The Parametric and Nonparametric Estimations of Normal Distribution for Mean Parameter

Abstract

This chapter's objective describes the point and interval estimations on the mean that is a part of the unknown parameter of normal distribution. The mean represents the distribution's central location or average, while the standard deviation measures the spread or variability of the data.   Point estimation involves providing a specific value to estimate a population parameter. The interval estimation provides a range or interval of values to estimate a population parameter, called a confidence interval. These estimations are estimated by the parametric method by using the maximum likelihood, Bayesian, and Markov Chain Monte Carlo methods. The nonparametric method consists of the bootstrap and the Jackknife methods. Maximum likelihood is the well-known method to approximate parameters because there are the properties of the unbiased estimator, consistency, and efficiency estimator. The Bayesian method is a statistical approach based on probability, prior, and posterior distribution. The Markov Chain Monte Carlo technique leverages Markov chains and random sampling to estimate complex probability distributions and involves the Bayesian method. The bootstrap and Jackknife methods are the resampling techniques by repeatedly drawing samples from the available data.