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The infimum values of two probability functions for the Gamma distribution
Ping Sun1, Ze-Chun Hu2, Wei Sun3
1Business School, Chengdu University, Chengdu, 610106 China.
Journal of Inequalities and Applications
|January 23, 2024
Summary
This study investigates infimum values for specific functions involving Gamma random variables. The research demonstrates a relationship between these infimum values and the standard normal random variable.
Area of Science:
- Probability Theory
- Statistical Inference
Background:
- The Gamma distribution is a key probability distribution in statistics.
- Understanding the behavior of functions involving random variables is crucial for statistical modeling.
Purpose of the Study:
- To determine the infimum values of two specific functions related to a Gamma random variable.
- To establish a connection between these infimum values and a standard normal random variable.
Main Methods:
- Mathematical analysis of functions involving a Gamma random variable.
- Derivation of infimum values using properties of probability distributions.
Main Results:
- The study derives the infimum values for the specified functions.
- It is shown that these infimum values are related to a standard normal random variable.
Conclusions:
- The findings provide insights into the extremal behavior of functions of Gamma random variables.
- This research contributes to the theoretical understanding of probability distributions and their associated functions.
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