An improvement in predictive modeling techniques with application to pivotal quantity and least square method

In this research, we develop a new method for predicting order data. Our approach involves selecting the best-fitting distribution through different tests, estimating its parameters, and constructing prediction intervals that leverage observed and predicted data. In this method, we entered the predicted data one by one, along with the observed data. At each step, we found a suitable distribution and then estimated its parameters and applied the prediction method, such as pivotal quantity and modified least square with cumulative hazard function. We implemented the new method using the R programming language and conducted comparative analyses against several established methods across datasets, encompassing health insurance coverage, glass fiber strength, and COVID-19 recovery rates. The results demonstrated this method's superior performance, particularly in terms of Mean square error (MSE) and coefficient of variation (CV), as well as its ability to predict more data and outperform traditional methods in most scenarios. This method has the ability to obtain a large number of predicted observations to reach about 150% to 200% of the real observations, as explained through a simulation study and real data.