Weibull Distribution Parameter Estimation for Statistical Data Analysis

This documentation presents a MATLAB-based methodology for estimating Weibull distribution parameters from statistical data, incorporating comprehensive three-parameter assessment and computation. The Weibull distribution, serving as a fundamental probability model, is widely utilized in reliability engineering and lifetime data analysis. Our approach employs maximum likelihood estimation (MLE) techniques to fit empirical data to the Weibull cumulative distribution function (CDF), optimizing for three critical parameters: shape parameter (β) governing distribution morphology, scale parameter (η) controlling characteristic life, and location parameter (γ) representing failure-free period. The implemented algorithm leverages MATLAB's statistical toolbox functions including wblfit for parameter estimation and wblplot for graphical goodness-of-fit validation. Key computational steps involve: 1) Data preprocessing and outlier handling using quantile-based filtering, 2) Iterative parameter optimization through Newton-Raphson numerical methods, and 3) Confidence interval calculation via bootstrapping techniques. The resultant parameters provide critical insights into data characteristics including failure rate patterns, reliability metrics, and hazard function behaviors. Accompanying MATLAB code examples demonstrate practical implementation with synthetic and real-world datasets, enabling users to adapt the methodology for their specific analytical requirements through customizable threshold settings and visualization options.