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A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data.

Ahtasham Gul1,2,3, Muhammad Mohsin1, Muhammad Adil2

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

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|April 6, 2021
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Summary
This summary is machine-generated.

A new four-parameter Weibull-Truncated Exponential Distribution (W-TEXPD) offers a flexible alternative for analyzing finite data. This novel truncated model demonstrates broad applicability across various datasets.

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Area of Science:

  • Probability and Statistics
  • Mathematical Modeling

Background:

  • Finite data analysis necessitates efficient truncated models.
  • Existing distributions may not optimally capture complex data characteristics.

Purpose of the Study:

  • To introduce a novel four-parameter distribution: the Weibull-Truncated Exponential Distribution (W-TEXPD).
  • To establish W-TEXPD as a versatile alternative to existing truncated distributions like Exponential, Weibull, and Gamma-Weibull.

Main Methods:

  • Derivation of key statistical properties: CDF, hazard function, moments, skewness, kurtosis, entropy.
  • Parameter estimation using the Maximum Likelihood Estimation (MLE) method.
  • Performance evaluation through a simulation study and fitting to diverse real-world datasets.

Main Results:

  • The W-TEXPD model's statistical characteristics were mathematically derived.
  • Simulation results demonstrated the model's parameter estimation capabilities.
  • The W-TEXPD showed strong performance when fitted to five distinct real-world datasets.

Conclusions:

  • The proposed W-TEXPD is a valuable and flexible tool for analyzing finite data.
  • The W-TEXPD offers superior performance compared to several existing truncated distributions.
  • The model's broad applicability across different fields is confirmed by empirical validation.