Size of the Bimodality by using Trapezoidal Rule

Abstract

This study investigates size of the bimodality to illustrate the gap between two modes/peaks in a bimodal distribution. To get this goal, one of the definite integral (i.e. Trapezoidal rule) is used on the mixture of normals (the mixture of one normal and the second one standard normal) with the selected parameter values of mean, mixing proportion and standard deviation. From the results, an increase of size of bimodality is identified if mean increases while all other parameters remain constant. A similar situation of increasing pattern of bimodality size has been observed when parametric values of mixing proportion increases (varies) while keeping other parameter values constant. However, a fraction changed is revealed in the size of bimodality if values of mean and mixing proportion are kept constant while standard deviation varies.