Uncertain Weibull regression model with imprecise observations

As an important growth curve model, Weibull regression model has been widely used in biological science, modern commerce, production industry and so on. However, due to technical constraints, loss of information, limited knowledge and other factors, and sometimes it is hard or impossible to accurately obtain enough observed data, which may make the classical Weibull regression models arrive at wrong conclusions in that these models ignored expressing such uncertainties behind the observed data. By considering this circumstance, a new modification of Weibull regression model for variables with imprecise observations is constructed to finish off this issue based on uncertainty theory. In addition, the parameter estimation method, residual analysis and confidence interval for the uncertain Weibull regression model are further presented, followed by leave-one-out cross-validation for model evaluation, to make the prediction or inference more reliable. Moreover, a numerical example is documented to illustrate how we construct the uncertain Weibull regression model step by step.