Parameter Estimation for the Truncated Weibull Model Using the Ordinary Differential Equation

In estimating the number of failures using the truncated data for the Weibull model, we often encounter a case that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease predictions, the SIR model described by simultaneous ordinary differential equations are often used, and this model can predict the final stage condition, i.e., the total number of infected patients, well, even if the number of observed data is small. These two models have the same condition for the observed data: truncated to the right. Thus, we have investigated whether the number of failures in the Weibull model can be estimated accurately using the ordinary differential equation. The positive results to this conjecture are shown.