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The comparison of parameters estimated from several different samples by maximum likelihood

|September 1, 1976

Summary

This study introduces computer programs for comparing sample parameters from populations with known distributions. The system facilitates hypothesis testing by performing maximum likelihood estimation and likelihood ratio tests.

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Area of Science:

Statistical computing
Computational statistics
Population genetics

Background:

Comparing parameters across multiple populations is crucial for statistical inference.
Existing methods may lack flexibility in handling arbitrary distribution functions.
The need for robust computational tools for parameter comparison is evident.

Purpose of the Study:

To develop a flexible computer program system for comparing parameters of samples from populations with known distributions.
To enable users to specify hypotheses regarding parameter equality under null and alternative conditions.
To provide tools for maximum likelihood estimation and likelihood ratio testing.

Main Methods:

Development of a computer program system using PL/I-FORM AC.

Related Experiment Videos

Implementation of maximum likelihood estimation for general and restricted models.

Calculation of statistics for likelihood ratio tests.

Main Results:

The developed system allows for the comparison of parameters across multiple populations with arbitrary distributions.
It supports user-defined hypotheses for parameter equality under null and alternative scenarios.
The system provides outputs necessary for conducting likelihood ratio tests, demonstrated with a numerical example.

Conclusions:

The developed computer program system offers a flexible and efficient approach to comparing population parameters.
It aids in hypothesis testing by integrating maximum likelihood estimation and likelihood ratio tests.
The system is applicable to statistical analyses involving populations with known, arbitrary distribution functions.