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Confidence interval, prediction interval and tolerance limits for a two-parameter Rayleigh distribution.

K Krishnamoorthy1, Dustin Waguespack1, Ngan Hoang-Nguyen-Thuy1

  • 1Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA.

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

This study introduces pivotal-based methods for estimating parameters and means of the two-parameter Rayleigh distribution. Maximum likelihood estimates (MLEs) offer slightly better performance for smaller sample sizes compared to moment and L-moments estimates.

Keywords:
Confidence intervalmoment estimatesprecisionprediction intervalquantile estimationtolerance interval

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • The two-parameter Rayleigh distribution is frequently used in modeling lifetime data and signal processing.
  • Accurate interval estimation of its parameters and mean is crucial for reliable predictions and decision-making.
  • Existing methods may lack precision, especially for smaller sample sizes.

Purpose of the Study:

  • To develop and evaluate novel pivotal-based methods for constructing confidence and prediction intervals for the two-parameter Rayleigh distribution.
  • To compare the performance of intervals derived from different estimation techniques: Maximum Likelihood Estimates (MLEs), Moment Estimates (MEs), and L-moments Estimates (L-MEs).
  • To provide practical guidelines for selecting the most appropriate estimation method based on sample size.

Main Methods:

  • Development of pivotal quantities derived from MLEs, MEs, and L-MEs for the two-parameter Rayleigh distribution.
  • Construction of confidence intervals for the mean, quantiles, and survival probability using these pivotal quantities.
  • Construction of prediction intervals for the mean of a future sample.
  • Performance evaluation through Monte Carlo simulation studies.
  • Illustration of the proposed methods with a real-world lifetime data example.

Main Results:

  • Pivotal-based methods were successfully developed for interval estimation.
  • Interval estimates derived from MEs and L-MEs demonstrated very similar performance.
  • Estimates based on MLEs showed slightly superior accuracy compared to MEs and L-MEs, particularly for small to moderate sample sizes.
  • The proposed methods were effectively demonstrated using lifetime data.

Conclusions:

  • The proposed pivotal-based methods provide effective tools for interval estimation in the two-parameter Rayleigh distribution.
  • MLEs are recommended for interval estimation when dealing with small to moderate sample sizes due to their enhanced accuracy.
  • MEs and L-MEs offer a viable alternative with comparable performance, especially for larger sample sizes.