Related Experiment Video
Updated: May 30, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Testing for seasonality using circular distributions based on non-negative trigonometric sums as alternative
J J Fernández-Durán1, M M Gregorio-Domínguez2
1Department of Statistics and School of Business, Instituto Tecnológico Autónomo de México, Río Hondo No. 1, Col. Progreso Tizapán, México jfdez@itam.mx.
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.
Related Concept Videos
Trigonometric Equations
Types of Hypothesis Testing
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5.
Trigonometric Functions of Real Numbers
Statistical Hypothesis Testing
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
The Anderson-Darling Test
Trigonometric Fourier series
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...