Normal Likelihood Maximization and Likelihood Plotting

Overview

This R program demonstrates the process of maximizing a normal likelihood function using the optim and optimize functions. It also includes functionality to plot the likelihood function for different scenarios.

Usage

Installation

1. Make sure you have R installed on your system. If not, you can download it from R Project.

2. Clone or download this repository to your local machine.

Running the Program

1. Open R or RStudio.

2. Set your working directory to the location where you have saved the program files.

3. Open the R script maximize_and_plot_normal_likelihood.R.

4. You can run the entire script or specific sections as needed.

Description

• make.NegLogLik function:

  • This function creates a negative log-likelihood function for a normal distribution.
  • Parameters:
    • data: The dataset for which you want to maximize the likelihood.
    • fixed: A vector indicating which parameters (mean and standard deviation) should be fixed during optimization.

• normals:

  • A random dataset generated using the rnorm function to serve as an example data for likelihood maximization.

• Estimating Parameters:

  • The script demonstrates two scenarios:
    1. Maximizing the likelihood to estimate both mean (mu) and standard deviation (sigma) using the optim function.
    2. Fixing one parameter (sigma or mu) and maximizing the likelihood for the other using the optimize function.

• Plotting The Likelihood:

  • The script includes examples of plotting the likelihood function for fixed parameters.
  • You can visualize how the likelihood changes for different parameter values.

Results

The script will output the estimated parameters (mu and sigma) or the optimized parameter value (in the case of fixed parameters) to the R console. Additionally, it will produce likelihood plots for the specified scenarios.

Dependencies

This program requires R to be installed on your system. There are no external packages or dependencies needed.

License

This program is provided under the MIT License.

Author

• [A.HAIDA]

Feel free to reach out if you have any questions or need further assistance.