MATLAB Source Code for Maximum Likelihood Estimation (MLE)

In statistics, Maximum Likelihood Estimation (MLE) is a widely used parameter estimation algorithm. This method infers the most probable parameter values that could generate observed data by analyzing their probability distribution. When these estimated parameters are treated as true values, they can be utilized for further statistical analysis. The MATLAB implementation typically involves defining a likelihood function based on the assumed probability distribution (e.g., normal, Poisson, or binomial) and optimizing it using built-in functions like `fminsearch` or `mle`. Key steps include: 1. Specifying the probability density function (PDF) for the data 2. Constructing the log-likelihood function to simplify calculations 3. Applying numerical optimization to find parameters maximizing likelihood 4. Validating results through confidence intervals or goodness-of-fit tests Researchers can leverage MATLAB's statistical toolbox for advanced MLE applications, including custom distribution modeling and hypothesis testing.