title: Stochastic monotony signature and biomedical applications.
abstract: We introduce a new concept, the stochastic monotony signature of a function, made of the sequence of the signs that indicate if the function is increasing or constant (sign +), or decreasing (sign -). If the function results from the averaging of successive observations with errors, the monotony sign is a random binary variable, whose density is studied under two hypotheses for the distribution of errors: uniform and Gaussian. Then, we describe a simple statistical test allowing the comparison between the monotony signatures of two functions (e.g., one observed and the other as reference) and we apply the test to four biomedical examples, coming from genetics, psychology, gerontology, and morphogenesis.
authors.affiliation: Laboratoire AGIM, FRE CNRS-UJF 3405, Faculté de médecine, Université Joseph-Fourier, 38700 La Tronche, France. Electronic address: Jacques.Demongeot@agim.eu.
authors.forename: Jacques
authors.initials: J
authors.lastname: Demongeot
authors.affiliation: Laboratoire AGIM, FRE CNRS-UJF 3405, Faculté de médecine, Université Joseph-Fourier, 38700 La Tronche, France.
authors.forename: Giuliana
authors.initials: G
authors.lastname: Galli Carminati
authors.affiliation: CERN, 1211 Genève 23, Switzerland.
authors.forename: Federico
authors.initials: F
authors.lastname: Carminati
authors.affiliation: Laboratoire AGIM, FRE CNRS-UJF 3405, Faculté de médecine, Université Joseph-Fourier, 38700 La Tronche, France; Université Grenoble Alpes, UFR SHS, BP 47, 38040 Grenoble cedex 09, France.
authors.forename: Mustapha
authors.initials: M
authors.lastname: Rachdi
mesh_terms: D013269:Stochastic Processes
keywords: Comparaison de fonctions; Comparison of functions; Monotony statistical test; Signature de monotonie aléatoire; Stochastic monotony signature; Test statistique de monotonie