Bayesian Unit-Lindley Model: Applications to Gasoline Yield and Risk Assessment Data

Weerinrada Wongrin; Sakuna Srianomai; Yuwadee Klomwises

doi:10.14456/nujst.2020.14

Authors

Weerinrada Wongrin Department of Statistics, Faculty of Science, Chiang Mai University, Mueang Chiang Mai, Chiang Mai, 50200
Sakuna Srianomai Department of Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Ladkrabang, Bangkok, 10520
Yuwadee Klomwises Department of Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Ladkrabang, Bangkok, 10520

DOI:

https://doi.org/10.14456/nujst.2020.14

Keywords:

rate data, Bayesian, Unit distribution, gasoline yield, risk assessment

Abstract

The regression model for the response variable with bounded domain is discussed. The baseline distribution called the unit Lindley distribution is considered. In the context of regression structure, the logit function is utilized with the unit Lindley model. Then, we have developed the Bayesian unit Lindley regression based on a frequently used prior. Additionally, we also investigate the specific prior for all standardized exploratory variables. The syntax of JAGS for the proposed model is included. In application study, the Bayesian unit Lindley regression is applied to two different datasets where response variables are associated with gasoline yield and risk assessment respectively. Based on the result of estimates and log-likelihood values, it is important to point out that the Bayesian unit-Lindley regression can improve the performance of the classical one.

References

Ali, S. (2015). On the Bayesian estimation of the weighted Lindley distribution. Journal of Statistical Computation and Simulation, 85, 855-880. https://doi.org/10.1080/00949655.2013.847442

Ali, S., Aslam, M., & Kazmi, S. M. A. (2013). A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution. Applied Mathematical Modelling, 37, 6068-6078. https://doi.org/10.1016/j.apm.2012.12.008

Branscum, A. J., Johnson, W. O., & Thurmond, M. C. (2007). Bayesian beta regression: applications to household expenditure data and genetic distance between foot‐and‐mouth disease viruses. Australian & New Zealand Journal of Statistics, 49(3), 287-301. https://doi.org/10.1111/j.1467-842X.2007.00481.x

Cribari-Neto, F., & Zeileis, A. (2009). Beta regression in R. Journal of Statistical Software, 34, 1-24. http://dx.doi.org/10.18637/jss.v034.i02

Dey, D. K., Ghosh, S. K. & Mallick, B. K. (2000). Generalized linear models: A Bayesian perspective. New York, USA: CRC Press.

Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y. S. (2008). A weakly informative default prior distribution for logistic and other regression models. The Annals of Applied Statistics, 2, 1360-1383. https://doi.org/10.1214/08-AOAS191

Ghitany, M. E., Atieh, B., & Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and computers in simulation, 78, 493-506. https://doi.org/10.1016/j.matcom.2007.06.007

Hand, D. J., Daly, F., McConway, K., Lunn, D., & Ostrowski, E. (1993). A handbook of small data sets. New York, USA: CRC Press.

Mazucheli, J., & Achcar, J. A. (2011). The Lindley distribution applied to competing risks lifetime data. Computer methods and programs in biomedicine, 104, 188-192.

Mazucheli, J., Menezes, A. F. B., & Chakraborty, S. (2019). On the one parameter unit-Lindley distribution and its associated regression model for proportion data. Journal of Applied Statistics, 46, 700-714. https://doi.org/10.1080/02664763.2018.1511774

Plummer, M., Best, N., Cowles. Kate., & Vines, K. (2006). CODA: Convergence Diagnosis and Output Analysis for MCMC. R News, 6, 7-11.

R Core Team. (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Retrieved from https://www.R-project.org/

Raqab, M. Z., Al-Jarallah, R. A., & Al-Mutairi, D. K. (2017). Closeness of Lindley distribution to Weibull and gamma distributions. Communications for Statistical Applications and Methods, 24, 129-142. https://doi.org/10.5351/CSAM.2017.24.2.129

Robert, C. P., Casella, G., & Casella, G. (2010). Introducing Monte Carlo methods with R. New York, USA: Springer.

Schmit, J. T., & Roth, K. (1990). Cost effectiveness of risk management practices. Journal of Risk and Insurance, 57, 455-470. http://doi.org/10.2307/252842

Shanker, R., Sharma, S., & Shanker, R. (2013). A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics, 4, 363-368. http://dx.doi.org/10.4236/am.2013.42056

Smithson, M., & Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological methods, 11, 54-71. https://doi.org/10.1037/1082-989X.11.1.54

Su, Y. S., & Yajima, M. (2015). R2jags: Using R to Run 'JAGS'. R package version 0.5-7. Retrieved from https://CRAN.R-project.org/package=R2jags