Uniqueness of one-parameter exponential curves fitted by non-linear least-squares to non-negative data in monotone non-increasing blocks

Abstract

For normalized non-negative data in monotone non-increasing blocks sufficiently close to test exponential functions computable in closed form, there is a unique one-parameter exponential decay curve fitted by weighted non-linear least squares. Upper and lower bounds in closed form bracket the optimal decay constant.

Keywords:

• Exponential curves
• uniqueness
• weighted nonlinear least squares

Acknowledgments

I thank the authors of Paolucci et al. (2017) for providing the data in Table 1. I thank the referees for a reference (Jukić and Scitovski 1997) and comments that improved the manuscript.

Additional information

Funding

This work was supported in part by a Professional Leave from Eastern Washington University.