Statistics and Its Interface

Volume 10 (2017)

Number 4

Fitting real data by means of non-homogeneous log-normal diffusion processes

Pages: 585 – 600

DOI: https://dx.doi.org/10.4310/SII.2017.v10.n4.a5

Authors

Patricia Román-Román (Dpto. Estadística e Investigación Operativa, Universidad de Granada, Spain)

Juan José Serrano-Pérez (Dpto. Estadística e Investigación Operativa, Universidad de Granada, Spain)

Francisco Torres-Ruiz (Dpto. Estadística e Investigación Operativa, Universidad de Granada, Spain)

Abstract

In order to achieve a good fit to real data that evolve over time and whose observed trend shows deviations with respect to an exponential shape, a non-homogeneous log-normal diffusion process with time dependent infinitesimal mean and variance is considered. Such model provides a more flexible structure of the variance than that of the non-homogeneous diffusion process only in its infinitesimal mean, allowing to reproduce the behaviour of the observed data more accurately and enable us to tackle problems in which data variability plays a fundamental role with a higher degree of reliability. A procedure for the estimation of the time functions included in the infinitesimal mean and variance is proposed and hypothesis testing to confirm or refute the need for considering non-homogeneous processes to fitting real data are designed. A simulation study corroborates the validity of the proposed estimation procedure. Finally, a real data application of a patient-derived xenograft (PDX) tumor model is performed.

Keywords

non-homogeneous log-normal diffusion process, fitting data, tumor growth

2010 Mathematics Subject Classification

Primary 60G99, 62M99. Secondary 62P10.

Published 30 May 2017