Related Experiment Video
Updated: Dec 9, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Weighted multimodal family of distributions with sine and cosine weight functions
Ayman Alzaatreh1, Jaber Kazempoor2, Adel Ahmadi Nadi2
1Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates.
Abstract:
In this paper, the moment of various types of sine and cosine functions are derived for any random variable. For an arbitrary even probability density function, the sine and cosine moments are used to define new families of univariate multimodal probability density and their corresponding characteristic functions. For illustration, two weighted multimodal generalizations of the t distribution are investigated. Furthermore, a method of calculating some interesting improper integrals is also presented. Finally, an explicit expression of the probability density function of the sum of independent t-distributed random variables with odd degrees of freedom is derived.
Related Concept Videos
Graphical and Analytic Representation of Sinusoids
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
Types of Functions II
Exponential and Sinusoidal Signals
Trigonometric Fourier series
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
Trigonometric Identities III
Direction Cosines of a Vector

