Statistical Estimates for Modified Gravitation Model by Aggregated Data

Abstract

A nonlinear regression model for forecasting of passenger flow between various spatial points (towns) is described. Unknown parameters are estimated using aggregated data when the information about a number of the departed passengers from each town is available only. For estimation, the least squares and maximum likelihood methods are used. Numerical examples are performed to illustrate the proposed approaches.

Keywords:

• Estimation
• Gradient method
• Information matrix
• Nonlinear regression

Mathematics Subject Classification:

• 62J02
• 62F10

Acknowledgments

This work was supported by grant 7326 of Latvian Ministry of Science and Education, and Riga Technical University: “Creation of mathematical models, algorithms and computer programs for Latvia's transport system's analysis, development prognosis and optimization.”

The authors wish to express their apprecation to anonymous reviewers for many helpful remarks on this article.