title: Testing for seasonality using circular distributions based on non-negative trigonometric sums as alternative hypotheses.
abstract: In medical and epidemiological studies, the importance of detecting seasonal patterns in the occurrence of diseases makes testing for seasonality highly relevant. There are different parametric and non-parametric tests for seasonality. One of the most widely used parametric tests in the medical literature is the Edwards test. The Edwards test considers a parametric alternative that is a sinusoidal curve with one peak and one trough. The Cave and Freedman test is an extension of the Edwards test that is also frequently applied and considers a sinusoidal curve with two peaks and two troughs as the alternative hypothesis. The Kuiper, Hewitt and David and Newell are common non-parametric tests. Fernández-Durán (2004) developed a family of univariate circular distributions based on non-negative trigonometric (Fourier) sums (series) (NNTS) that can account for an arbitrary number of peaks and troughs. In this article, this family of distributions is used to construct a likelihood ratio test for seasonality considering parametric alternative hypotheses that are NNTS distributions.
authors.affiliation: Department of Statistics and School of Business, Instituto Tecnológico Autónomo de México, Río Hondo No. 1, Col. Progreso Tizapán, México jfdez@itam.mx.
authors.forename: J J
authors.initials: JJ
authors.lastname: Fernández-Durán
authors.affiliation: Department of Actuarial Science, Instituto Tecnológico Autónomo de México, Río Hondo No. 1, Col. Progreso Tizapán, México.
authors.forename: M M
authors.initials: MM
authors.lastname: Gregorio-Domínguez
mesh_terms: D058872:Epidemics; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D012621:Seasons