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Statistical model for analizing negative variables with application to compression test on concrete

10.24050/reia.v19i38.1526
Published 2022-06-01
Articles

Abstract

In some areas of knowledge, we can find negative variables (ℝ-), to have a statistical model is crucial to represent the phenomenon and explain it using other variables. This paper proposes a regression model to analyze negative random variables using the reflected Weibull distribution. We developed the RelDists package in the R programming language to implement the proposed model. A Monte Carlo simulation study was conducted to explore the performance of the estimation procedure considering censored and uncensored data and the presence and absence of covariates. From the simulation study, we found that the estimation procedure achieves accurate estimations of the parameters as the sample size increases and the percentage of censoring decreases. In the paper, we present an application of the proposed model using experimental data from a compression test with concrete specimens. In the application, a model was fitted to explain the shrinkage strain using the variable time. The regression model for negative variables and the RelDists package can be used by academic, scientific, and business communities to perform reliability analysis.

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Authors

  • Olga Usuga

    Universidad de Antioquia

  • Carmen Patiño Rodríguez

  • Freddy Hernández Barajas

  • Amylkar Urrea Montoya

References

Akaike, H. (1983). Information measures and model selection. Int Stat Inst, 44, 277–291.

Al Abbasi, J. N., Risan, H. K., & Resen, I. A. (2018). Application of Kumaraswamy Extreme Values Distributions to Earthquake Magnitudes in Iraq and Conterminous Regions. International Journal of Applied Engineering Research, 13(11), 8971–8980.

Ali, M. M., & Woo, J. (2006). Skew-symmetric reflected distributions. Soochow Journal of Mathematics, 32(2), 233–240. https://doi.org/10.1080/01966324.2008.10737716

Almalki, S. J., & Nadarajah, S. (2014). Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety, 124(4), 32–55. https://doi.org/https://doi.org/10.1016/j.ress.2013.11.010

Balakrishnan, N., & Kocherlakota, S. (1985). On the double Weibull distribution: order statistics and estimation. Sankhya: The Indian Journal of Statistics, Series B, 47(2), 161–178.

Barreto-Souza, W., Santos, A. H. S., & Cordeiro, G. M. (2010). The beta generalized exponential distribution. Journal of Statistical Computation and Simulation, 80(2), 159–172. https://doi.org/10.1080/00949650802552402

Caron, R., Sinha, D., Dey, D., & Polpo, A. (2017). Categorical data analysis using a skewed Weibull regression model. In arXiv (Vol. 20, Issue 3, pp. 176–193). Multidisciplinary Digital Publishing Institute. https://doi.org/https://doi.org/10.3390/e20030176

Cohen, A. C. (1975). Multi-censored sampling in the three parameter Weibull distribution. Technometrics, 17(3), 347–351. https://doi.org/https://doi.org/10.2307/1268072

Cohen, A. C. (2016). Truncated and censored samples: theory and applications. CRC press.

Cohen, C. A., & Whitten, B. (1982). Modified maximum likelihood and modified moment estimators for the three-parameter Weibull distribution. Communications in Statistics-Theory and Methods, 11(23), 2631–2656. https://doi.org/https://doi.org/10.1080/03610928208828412

Dunn, P. K., & Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5(3), 236–244. https://doi.org/https://doi.org/10.2307/1390802

Gibbons, D. I., & Vance, L. C. (1983). Estimators for the 2-parameter Weibull distribution with progressively censored samples. IEEE Transactions on Reliability, 32(1), 95–99. https://doi.org/10.1109/TR.1983.5221484

Guure, C. B., & Ibrahim, N. A. (2012). Bayesian analysis of the survival function and failure rate of Weibull distribution with censored data. Mathematical Problems in Engineering, 2012. https://doi.org/https://doi.org/10.1155/2012/329489

Guure, C. B., & Ibrahim, N. A. (2013). Methods for estimating the 2-parameter Weibull distribution with type-I censored data. Research Journal of Applied Sciences, Engineering and Technology, 5(3), 689–694. https://doi.org/10.19026/rjaset.5.5010

Hernández, B. F., Cano, B. U., & Caicedo, E. A. C. (2021). Modelos GAMLSS para analizar el grado secado de calcio dihidratado. Revista EIA, 18(35), 1–13. https://doi.org/https://doi.org/10.24050/reia.v18i35.1439

Huang, H., Garcia, R., Huang, S.-S., Guadagnini, M., & Pilakoutas, K. (2019). A practical creep model for concrete elements under eccentric compression. Materials and Structures, 52(6), 1–18. https://doi.org/10.1617/s11527-019-1432-z

Kalsoom, U., Nasir, W., & Syed, A. (2019). On estimation of reflected Weibull distribution using bayesian analysis under informative prior. 15th Islamic Countries Conference on Statistical Sciences (ICCS-15), 49.

Kim, C., Jung, J., & Chung, Y. (2011). Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring. Statistical Papers, 52(1), 53–70. https://doi.org/https://doi.org/10.1007/s00362-009-0203-2

Kim, J. S., & Yum, B.-J. (2008). Selection between Weibull and lognormal distributions: A comparative simulation study. Computational Statistics & Data Analysis, 53(2), 477–485. https://doi.org/https://doi.org/10.1016/j.csda.2008.08.012

Lai, C.-D. (2014). Generalized weibull distributions. Springer.

Lee, C., Famoye, F., & Olumolade, O. (2007). Beta-Weibull distribution: some properties and applications to censored data. Journal of Modern Applied Statistical Methods, 6(1), 173–186. https://doi.org/DOI: 10.22237/jmasm/1177992960

Meeker, W. Q., & Escobar, L. A. (2014). Statistical methods for reliability data. John Wiley & Sons.

Modarres, M., Kaminskiy, M. P., & Krivtsov, V. (2016). Reliability engineering and risk analysis: a practical guide. CRC press.

Morris, T. P., White, I. R., & Crowther, M. J. (2019). Using simulation studies to evaluate statistical methods. Statistics in Medicine, 38(11), 2074–2102. https://doi.org/https://doi.org/10.1002/sim.8086

Nagatsuka, H., Kamakura, T., & Balakrishnan, N. (2013). A consistent method of estimation for the three-parameter Weibull distribution. Computational Statistics & Data Analysis, 58(1), 210–226. https://doi.org/https://doi.org/10.1016/j.csda.2012.09.005

Nagelkerke, N. J. D. (1991). A Note on a General Definition of the Coefficient of Determination. Biometrika, 78(3), 691–692. https://doi.org/https://doi.org/10.1093/biomet/78.3.691

Odell, P. M., Anderson, K. M., & D’Agostino, R. B. (1992). Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model. Biometrics, 48(3), 951–959.

Orjubin, G. (2007). Maximum field inside a reverberation chamber modeled by the generalized extreme value distribution. IEEE Transactions on Electromagnetic Compatibility, 49(1), 104–113. https://doi.org/10.1109/TEMC.2006.888172

Phadnis, M. A., Sharma, P., Thewarapperuma, N., & Chalise, P. (2020). Assessing accuracy of Weibull shape parameter estimate from historical studies for subsequent sample size calculation in clinical trials with time-to-event outcome. Contemporary Clinical Trials Communications, 17(1). https://doi.org/10.1016/j.conctc.2020.100548

R Core Team. (2021). R: A Language and Environment for Statistical Computing. https://www.r-project.org/

Regal, R. R., & Larntz, K. (1978). Likelihood methods for testing group problem solving models with censored data. Psychometrika, 43(3), 353–366. https://doi.org/https://doi.org/10.1007/BF02293645

Rigby, R. A., & Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3), 507–554. https://doi.org/https://doi.org/10.1111/j.1467-9876.2005.00510.x

Ross, M. S. (2012). Simulation. Elsevier.

Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.

Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of Mathematical Statistics, 33(3), 1187–1192.

Stasinopoulos, M. D., Rigby, R. A., Heller, G. Z., Voudouris, V., & Bastiani, F. (2017). Flexible Regression and Smoothing Using GAMLSS in R. CRC Press.

Wei, Z., Start, M., Hamilton, J., & Luo, L. (2016). A unified framework for representing product validation testing methods and conducting reliability analysis. SAE International Journal of Materials and Manufacturing, 9(2), 303–314. https://doi.org/https://doi.org/10.4271/2016-01-0269

Xie, M., & Lai, C. D. (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering & System Safety, 52(1), 87–93. https://doi.org/https://doi.org/10.1016/0951-8320(95)00149-2

Zhang, T., & Xie, M. (2007). Failure data analysis with extended Weibull distribution. Communications in Statistics—Simulation and Computation®, 36(3), 579–592. https://doi.org/https://doi.org/10.1080/03610910701236081

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