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 language | English (US) |
|---|---|
| Pages (from-to) | 75-80 |
| Number of pages | 6 |
| Journal | Model Assisted Statistics and Applications |
| Volume | 6 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2011 |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - Bayesian credible intervals for monitoring liquid blending rates
AU - Rahardja, Dewi
AU - Zhao, Yan D.
AU - Xie, Xian Jin
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Bayesian credible interval
KW - confidence interval
KW - Fieller's method
KW - liquid blending rate
KW - power exponential distribution
UR - http://www.scopus.com/inward/record.url?scp=79957705122&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79957705122&partnerID=8YFLogxK
U2 - 10.3233/MAS-2011-0175
DO - 10.3233/MAS-2011-0175
M3 - Article
AN - SCOPUS:79957705122
VL - 6
SP - 75
EP - 80
JO - Model Assisted Statistics and Applications
JF - Model Assisted Statistics and Applications
SN - 1574-1699
IS - 2
ER -