  The modality is important topic for modelling. Using parametric models is an
efficient way when real data set shows trimodality. In this paper we propose a
new class of trimodal probability distributions, that is, probability
distributions that have up to three modes. Trimodality itself is achieved by
applying a proper transformation to density function of certain continuous
probability distributions. At first, we obtain preliminary results for an
arbitratry density function $g(x)$ and, next, we focus on the Gaussian case,
studying trimodal Gaussian model more deeply. The Gaussian distribution is
applied to produce the trimodal form of Gaussian known as normal distribution.
The tractability of analytical expression of normal distribution, and
properties of the trimodal normal distribution are important reasons why we
choose normal distribution. Furthermore, the existing distributions should be
improved to be capable of modelling efficiently when there exists a trimodal
form in a data set. After new density function is proposed, estimating its
parameters is important. Since Mathematica 12.0 software has optimization tools
and important modelling techniques, computational steps are performed by using
this software. The bootstrapped form of real data sets are applied to show the
modelling ability of the proposed distribution when real data sets show
trimodality.
