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一种模拟地震次数的新方法：INARPQX(1) 过程。

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

作者信息

Altun Emrah, Bhati Deepesh, Khan Naushad Mamode

机构信息

Department of Mathematics, Bartin University, 74100 Bartin, Turkey.

Department of Statistics, Central University of Rajasthan, Ajmer, India.

出版信息

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

DOI:10.1007/s42452-020-04109-8
PMID:33554048
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7856626/
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.

摘要

本文介绍了一种具有新的创新分布的一阶整数值自回归过程，简称为INARPQX(1)过程。通过将泊松分布与拟x伽马分布混合得到一种新的创新分布。详细研究了新分布的统计性质和估计过程。用条件最大似然法和尤尔-沃克法两种估计方法讨论了INARPQX(1)过程的参数估计。将提出的INARPQX(1)过程应用于地震月计数时间序列。实证结果表明，INARPQX(1)过程是对计数的过度分散时间序列进行建模的重要过程，可用于预测震级大于4级的地震数量。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/e4ff8d068ef9/42452_2020_4109_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/9fa1c71a9ab8/42452_2020_4109_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/737a655f91dd/42452_2020_4109_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/8eafbd85227b/42452_2020_4109_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/e24a5ca00d77/42452_2020_4109_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/ad4c552f789e/42452_2020_4109_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/e4ff8d068ef9/42452_2020_4109_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/9fa1c71a9ab8/42452_2020_4109_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/737a655f91dd/42452_2020_4109_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/8eafbd85227b/42452_2020_4109_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/e24a5ca00d77/42452_2020_4109_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/ad4c552f789e/42452_2020_4109_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/262d/7856626/e4ff8d068ef9/42452_2020_4109_Fig9_HTML.jpg

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本文引用的文献

1
Analysis of worldwide earthquake mortality using multivariate demographic and seismic data.利用多元人口统计和地震数据对全球地震死亡率进行分析。
Am J Epidemiol. 2005 Jun 15;161(12):1151-8. doi: 10.1093/aje/kwi149.