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Testing exponentiality based on the extropy of record values.

Peihan Xiong1, Weiwei Zhuang1, Guoxin Qiu1,2

  • 1Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new goodness-of-fit test for exponential distribution using extropy of record values. The proposed test demonstrates superior power for certain failure rate distributions, particularly with small sample sizes.

Keywords:
62B10Adjusted powerMonte Carlo simulationPrimary 62G30Secondary 63E10exponentiality testextropyrecord value

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • The exponential distribution is fundamental in statistical modeling, particularly for reliability and survival analysis.
  • Characterizing distributions and developing robust goodness-of-fit tests are crucial for accurate data analysis.
  • Extropy, a measure of information, offers a novel perspective for distribution characterization.

Purpose of the Study:

  • To characterize the exponential distribution using the extropy of record values.
  • To introduce a new goodness-of-fit test for exponentiality based on this characterization.
  • To evaluate the performance of the proposed test against existing methods.

Main Methods:

  • Characterization of the exponential distribution via extropy of record values.
  • Development of a novel goodness-of-fit test statistic.
  • Monte Carlo simulations to determine critical values and power analysis.
  • Comparison with 58 existing tests using adjusted power against various alternatives.

Main Results:

  • The proposed test is characterized by the extropy of record values.
  • Monte Carlo simulations provide critical values for practical application.
  • The new test exhibits superior adjusted power against alternatives with increasing failure rates or bathtub-shaped decreasing-increasing failure rates.
  • This advantage is particularly pronounced for small sample sizes.

Conclusions:

  • The proposed goodness-of-fit test offers a valuable new tool for assessing exponentiality.
  • The test is robust and performs well, especially in scenarios with specific failure rate patterns and limited data.
  • The findings contribute to the advancement of statistical testing methodologies in reliability and related fields.