Bayesian credible intervals for monitoring liquid blending rates

Dewi Rahardja, Yan D. Zhao, Xian Jin Xie

Research output: Contribution to journalArticle

Abstract

We consider the problem of constructing confidence intervals (CIs) for the blending coefficient of different liquid, such as the blended underground storage tank (UST) leak data for compliance. For this problem, confidence intervals based on Fieller's Method have been proposed. This method utilizes a blending coefficient estimator which is a ratio of two correlated normal random variables. However, this method assumes normally distributed random errors in the UST leak model and therefore may be inappropriate for the UST leak data which typically have heavy-tailed empirical distributions. In this paper we develop a Bayesian approach assuming non-normal random errors with the Power Exponential Distribution (PED). A real-data example using Cary blended site data is given to illustrate both the Fieller's CIs and the Bayesian credible intervals. Monte Carlo simulations are conducted to compare the coverage probability and average width of CIs for both methods. For data with heavy-tailed distributions, the simulations show that both Fieller's and Bayesian intervals perform adequately in terms of coverage. However, Bayesian intervals perform better in terms of yielding CIs with shorter expected width.

Original languageEnglish (US)
Pages (from-to)75-80
Number of pages6
JournalModel Assisted Statistics and Applications
Volume6
Issue number2
DOIs
StatePublished - 2011

Fingerprint

Credible Interval
Random errors
Confidence interval
Liquid
Monitoring
Liquids
Random variables
Heavy-tailed Distribution
Random Error
Exponential Power Distribution
Interval
Empirical Distribution
Coverage Probability
Coefficient
Bayesian Approach
Compliance
Coverage
Monte Carlo Simulation
Random variable
Estimator

Keywords

  • Bayesian credible interval
  • confidence interval
  • Fieller's method
  • liquid blending rate
  • power exponential distribution

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Statistics and Probability

Cite this

Bayesian credible intervals for monitoring liquid blending rates. / Rahardja, Dewi; Zhao, Yan D.; Xie, Xian Jin.

In: Model Assisted Statistics and Applications, Vol. 6, No. 2, 2011, p. 75-80.

Research output: Contribution to journalArticle

Rahardja, Dewi ; Zhao, Yan D. ; Xie, Xian Jin. / Bayesian credible intervals for monitoring liquid blending rates. In: Model Assisted Statistics and Applications. 2011 ; Vol. 6, No. 2. pp. 75-80.
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