A new approach to model the counts of earthquakes: INARPQX(1) process

Emrah Altun; Deepesh Bhati; Naushad Mamode Khan

doi:10.1007/s42452-020-04109-8

A new approach to model the counts of earthquakes: INARPQX(1) process

SN Appl Sci. 2021;3(2):274. doi: 10.1007/s42452-020-04109-8. Epub 2021 Feb 3.

Authors

Emrah Altun¹, Deepesh Bhati², Naushad Mamode Khan³

Affiliations

¹ Department of Mathematics, Bartin University, 74100 Bartin, Turkey.
² Department of Statistics, Central University of Rajasthan, Ajmer, India.
³ Department of Economics and Statistics, University of Mauritius, Reduit, Mauritius.

Abstract

This paper introduces a first-order integer-valued autoregressive process with a new innovation distribution, shortly INARPQX(1) process. A new innovation distribution is obtained by mixing Poisson distribution with quasi-xgamma distribution. The statistical properties and estimation procedure of a new distribution are studied in detail. The parameter estimation of INARPQX(1) process is discussed with two estimation methods: conditional maximum likelihood and Yule-Walker. The proposed INARPQX(1) process is applied to time series of the monthly counts of earthquakes. The empirical results show that INARPQX(1) process is an important process to model over-dispersed time series of counts and can be used to predict the number of earthquakes with a magnitude greater than four.

Keywords: Discrete distribution; Earthquake; INAR(1) process; Over-dispersion.