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Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions.

Heliyon·2021
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Inverse Lomax-Rayleigh distribution with application.

Jamilu Yunusa Falgore1, Muhammad Nazir Isah1, Hussein Ahmad Abdulsalam1

  • 1Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.

Heliyon
|November 29, 2021
PubMed
Summary
This summary is machine-generated.

A new Inverse Lomax Rayleigh (ILR) distribution was developed. Simulation and fatigue data analysis show ILR estimates are unbiased, consistent, efficient, and outperform other distributions.

Keywords:
Inverse Lomax GInverse Lomax RayleighMomentsProbability distributionT-X approach

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Area of Science:

  • Statistics
  • Probability Distributions

Background:

  • The Rayleigh distribution is widely used in various fields.
  • There is a need for more flexible statistical distributions to model complex data.

Purpose of the Study:

  • To propose a new flexible statistical distribution, the Inverse Lomax Rayleigh (ILR) distribution.
  • To derive key mathematical properties of the ILR distribution.
  • To evaluate the performance of ILR using simulation and real-world data.

Main Methods:

  • The Inverse Lomax generator was used to extend the Rayleigh distribution.
  • Mathematical derivations for moments, entropy, order statistics, and quantile function were performed.
  • A simulation study assessed the properties of ILR estimates.
  • The ILR distribution was applied to fatigue data.

Main Results:

  • The complete and incomplete moments, entropy, distribution of order statistics, and quantile function of the ILR distribution were derived.
  • Simulation results indicated that ILR estimates are unbiased, consistent, and efficient.
  • Application to fatigue data demonstrated the flexibility and superior performance of the ILR distribution compared to other models.

Conclusions:

  • The proposed Inverse Lomax Rayleigh (ILR) distribution offers a flexible and effective alternative for modeling data.
  • The ILR distribution exhibits desirable statistical properties and performs well in practical applications, particularly for fatigue analysis.