A general class of trimodal distributions: properties and inference

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