Skew multimodal normal distribution


Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran.


In this paper the multimodal normal distribution is introduced. This distribution is a generalization of the standard normal distribution and covers the symmetric distributions with up to three modes. Then the skew multimodal normal distribution is introduced as a skewed-symmetric distribution generated by the standard normal distribution. Some properties of this distribution are investigated. Data generation methods from this distribution are proposed and its location and scale distribution is introduced. The maximum likelihood estimates of the parameters are studied and evaluated using simulations. The famous geyser dataset is fitted to this distribution and compared with several competing distributions.


Main Subjects

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Volume 11, Issue 2
June 2021
Pages 382-399
  • Receive Date: 03 December 2020
  • Revise Date: 26 April 2021
  • Accept Date: 15 May 2021
  • First Publish Date: 03 June 2021