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Related Experiment Video

Updated: Aug 24, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Published on: July 3, 2020

Ratio of Two Independent Lindley Random Variables.

Mohammad Shakil¹, Aneeqa Khadim², Aamir Saghir³

¹Department of Mathematics, Miami Dade College, Hialeah, FL USA.

Journal of Statistical Theory and Applications : JSTA

|October 21, 2022

Summary

A new distribution for the ratio of two independent Lindley random variables was developed. This novel distribution demonstrated superior fitting to COVID-19 and bladder cancer data compared to existing Lindley variations.

Keywords:

Characterizations Estimation Lindley distribution Ratio of independent random variables

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Area of Science:

Statistics
Probability Distributions
Biostatistics

Background:

The Lindley distribution is a flexible model for skewed data.
Analyzing ratios of random variables is crucial in various scientific fields.
Existing Lindley distribution variations have limitations in certain applications.

Purpose of the Study:

Derive and characterize the distribution of the ratio of two independent Lindley random variables with different parameters.
Evaluate the performance of the proposed ratio distribution using real-world data.
Compare the proposed distribution with existing right-skewed Lindley distribution models.

Main Methods:

Mathematical derivation of the probability distribution for the ratio of two independent Lindley random variables.
Analysis of the distributional properties of the derived ratio distribution.
Fitting the proposed distribution and comparative models to COVID-19 and bladder cancer datasets.

Main Results:

The distribution of the ratio of two independent Lindley random variables was successfully derived.
The proposed ratio distribution exhibited a better fit to the COVID-19 and bladder cancer data.
The new distribution outperformed several well-known right-skewed Lindley distribution variants.

Conclusions:

The proposed ratio distribution offers an improved model for analyzing skewed data, particularly in biostatistical applications.
This new distribution provides a valuable alternative for modeling ratios of independent Lindley variables.
The findings suggest the utility of the proposed distribution in fields like epidemiology and medical research.