The flexible transmuted record type-scale mixture of normal family and its AR(1) extension

Authors

  • Atefeh Zarei Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
  • Zahra Khodadadi Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran.
  • Hediyeh Jafarpour Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
  • Mohsen Malaki Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran

Keywords:

AR(1) process, COVID-19 data set, ECME algorithm, Scale mixture of normal, Transmuted record type.

Abstract

In the present paper, a flexible skew version of the scale mixture of normal
family is introduced based on the transmuted record type, called TRT-SMN, which seems  suitable for handling any skewness and kurtosis in real data sets. Several properties of  the TRT-SMN family are provided, including the moment generating function and r-th  moments. The parameters of the new family are estimated through the ECME algorithm.  Further to the elegant properties of the proposed family, the paper considers, in the time series context, a first-order autoregressive process with TRT-SMN distributed innovations. Some Monte Carlo simulation experiments are executed to assess the consistency of the ECME estimates. To further motivate its purpose, the proposed process is applied to analyze the series of COVID-19 incidence in Bavaria. The proposed AR(1) with TRT-SMN innovations yields superior fitting criteria compared to AR(1) process
with Gaussian innovations.

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Published

2023-02-04

Issue

Vol. 17

Section

Vol. 17, No. 2, (2023)

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