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Estimation of the probability content in a specified interval using fiducial approach
Ngan Hoang-Nguyen-Thuy1, K Krishnamoorthy1
1Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA.
Journal of Applied Statistics
|June 16, 2022
Summary
New statistical methods provide exact and approximate confidence intervals for probability content within specified intervals. These fiducial-based solutions apply to various location-scale distributions, aiding in quality control estimations.
Area of Science:
- Statistics
- Probability Theory
- Quality Control
Background:
- Accurate estimation of probability content within intervals is crucial for quality control.
- Existing statistical methods may have limitations for certain distributions.
Purpose of the Study:
- To propose novel statistical methods for constructing confidence intervals for probability content.
- To develop exact and approximate solutions using the fiducial approach.
- To illustrate the application of these methods with engineering examples.
Main Methods:
- Development of fiducial-based statistical methods.
- Application to location-scale and log-location-scale distributions.
- Specific methods detailed for normal, Weibull, two-parameter exponential, and two-parameter Rayleigh distributions.
Main Results:
- Exact and approximate confidence interval solutions are derived.
- The merits of each solution are evaluated for different distributions.
- Practical examples demonstrate the estimation of product compliance percentages.
Conclusions:
- The proposed statistical methods offer effective tools for confidence interval construction.
- Fiducial-based approaches provide viable solutions for probability content estimation.
- The methods are applicable to real-world engineering quality assessment scenarios.
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