The Balanced Discrete Weibull Distribution and Its Corresponding Integer-value Autoregressive Model: Properties, Estimation and Analysis of Counting Death of COVID-19 Data

Document Type : Original Paper

Authors

Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

In this paper, we introduce a new discrete Weibull distribution based on the balanced discretization method, which preserves the partial moments between the two discrete and continuous versions

of the distributions. Some statistical features of the new distribution and different kinds of dispersion of

the proposed distribution are presented based on various selections of parameters. In addition to introducing the new version of balanced discrete Weibull, we provide the integer-valued autoregressive model

with the innovation of the proposed discrete distribution and evaluate different methods for estimating the

model parameters. Using the counts of death of the COVID-19 data in Cuba, Malawi and Uzbekistan, we

appraise the performance of the new process in fitting real data to some classical integer-valued autoregressive models. Finally, the forecasting of the process is checked based on real data using both classical

and sieve bootstrap approaches

Keywords

Main Subjects

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History

• Receive Date: 08 April 2022
• Revise Date: 01 August 2022
• Accept Date: 13 August 2022