The Likelihood Estimator Tool is an interactive and data-driven solution designed to help researchers, analysts, and decision-makers estimate parameters of statistical models using the likelihood function. This tool allows users to input observed data and a probability distribution (e.g., Normal, Binomial, Poisson) to compute maximum likelihood estimates (MLEs) for model parameters. It provides actionable insights into parameter estimation, goodness-of-fit, and confidence intervals, enabling stakeholders to make informed decisions.

Key Features:

1. Dynamic Input Fields: Users can input observed data and select a probability distribution (e.g., Normal, Binomial, Poisson).
2. Maximum Likelihood Estimation (MLE): Automatically compute MLEs for model parameters based on user inputs.
3. Goodness-of-Fit Metrics: Calculate metrics such as log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC).
4. Interactive Charts: Visualize likelihood functions, fitted distributions, and confidence intervals using line graphs or histograms for enhanced clarity.
5. Scenario Testing: Allow users to adjust inputs dynamically to explore how changes in data or distribution affect parameter estimates.
6. PDF Export Functionality: Generate downloadable reports summarizing likelihood estimation results for presentations or sharing with stakeholders.
7. Modern and Stylish Design: A sleek interface with vibrant colors, animations, and clear typography to enhance user engagement.
8. Fully Responsive: Optimized for all devices, ensuring seamless functionality on desktops, tablets, and mobiles.
9. Self-Contained Container: The tool operates within its own container, ensuring no interference with the page header or footer.

Use Cases:

• Researchers estimating parameters of statistical models for experimental data.
• Data scientists fitting probabilistic models to real-world datasets.
• Academics teaching concepts like likelihood estimation, MLE, and model selection criteria.

How It Works:
Users input observed data and select a probability distribution (e.g., Normal, Binomial, Poisson). The tool computes maximum likelihood estimates (MLEs) for the parameters of the selected distribution and calculates goodness-of-fit metrics such as log-likelihood, AIC, and BIC. Results are displayed in tables and visualizations, allowing users to interpret the likelihood function and fitted distribution. Users can customize inputs dynamically, analyze scenarios, and download detailed reports in PDF format for further analysis or sharing with stakeholders.