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Truncated Weibull-exponential distribution: methods and applications.

Salman Abbas¹, Muhammad Farooq¹, Jumanah Ahmed Darwish²

¹Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.

Scientific Reports

|November 27, 2023

Summary

This summary is machine-generated.

This study introduces a new truncated Weibull-exponential distribution, detailing its mathematical properties and reliability measures. Simulation and real-world data analysis confirm its utility in statistical modeling.

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Area of Science:

Statistics
Probability Theory
Mathematical Modeling

Background:

The Weibull-exponential distribution is a flexible model, but its truncated versions require further investigation.
Understanding the mathematical properties of probability distributions is crucial for accurate data analysis.

Purpose of the Study:

Introduce and analyze a novel truncated Weibull-exponential distribution.
Explore its mathematical characteristics, including moments, generating functions, and entropy.
Evaluate its reliability measures and practical applicability.

Main Methods:

Derivation of key mathematical properties: moments, generating functions, inverse distribution function, and entropy.
Development and application of reliability measures.
Simulation study to assess the stability of maximum likelihood estimates (MLEs).
Application to two real-world social science datasets.

Main Results:

The mathematical properties of the truncated Weibull-exponential distribution were thoroughly derived.
Reliability measures were analyzed, providing insights into its behavior.
Simulation results demonstrated the stability and consistency of the MLEs.
The distribution showed relevance in modeling social science data.

Conclusions:

The truncated Weibull-exponential distribution offers a valuable addition to the statistical modeling toolkit.
Its mathematical properties and demonstrated applicability support its use in diverse fields.
Further research can explore extensions and applications of this novel distribution.