Formulation of confidence intervals for estimated actual distances

We devise a new method to calculate the confidence intervals for estimated actual distances. For that purpose, we first develop a prediction error related random variable which is both homoscedastic and normally distributed, and then we use this random variable to devise the confidence interval. Using this method, we develop confidence intervals for two distance predicting functions known as ordinary and weighted sums of order p. We also compare the prediction accuracy of these two distance functions using these confidence intervals and actual distance data from 17 geographical regions. We find that better confidence intervals for the estimated actual distances can be obtained with the weighted sum of order p than the ordinary sum of order p.