Statistical model for analizing negative variables with application to compression test on concrete (2022)
ABSTRACT: In some areas of knowledge, we can find phenomena represented by negative variables (R# ) ; having a statistical model is crucial to describe the phenomenon and explain it using other variables. This paper proposes a regression model to analyze negative random variables using the reflected Weibull distribution. This paper reports the RelDists package created 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. The simulation study encompasses two cases: without covariates and with covariables. In the first case, we only have the response variable to estimate the distribution parameters. In the second case, we have the response variable and two explanatory variables to estimate the model parameters. Additionally, censored and uncensored data were considered in the simulation study. 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.