Estimation method of mixture distribution and modeling of COVID-19 pandemic

Tabassum Naz Sindhu; Zawar Hussain; Naif Alotaibi; Taseer Muhammad; Tabassum Naz Sindhu; Zawar Hussain; Naif Alotaibi; Taseer Muhammad

doi:10.3934/math.2022554

AIMS Mathematics

2022, Volume 7, Issue 6: 9926-9956. doi: 10.3934/math.2022554

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Estimation method of mixture distribution and modeling of COVID-19 pandemic

1.
Department of Statistics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan
2.
Department of Social & Allied Sciences, Cholistan University of Veterinary & Animal Sciences, Bahawalpur 63100, Pakistan
3.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Kingdom of Saudi Arabia
4.
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia

Received: 21 August 2021 Revised: 18 December 2021 Accepted: 17 January 2022 Published: 21 March 2022
MSC : 62E10, 62E15, 62F10

The mathematical characteristics of the mixture of Lindley model with 2-component (2-CMLM) are discussed. In this paper, we investigate both the practical and theoretical aspects of the 2-CMLM. We investigate several statistical features of the mixed model like probability generating function, cumulants, characteristic function, factorial moment generating function, mean time to failure, Mills Ratio, mean residual life. The density, hazard rate functions, mean, coefficient of variation, skewness, and kurtosis are all shown graphically. Furthermore, we use appropriate approaches such as maximum likelihood, least square and weighted least square methods to estimate the pertinent parameters of the mixture model. We use a simulation study to assess the performance of suggested methods. Eventually, modelling COVID-19 patient data demonstrates the effectiveness and utility of the 2-CMLM. The proposed model outperformed the two component mixture of exponential model as well as two component mixture of Weibull model in practical applications, indicating that it is a good candidate distribution for modelling COVID-19 and other related data sets.
- mixture model,
- least square estimation,
- Mills Ratio,
- weighted least square estimation
Citation: Tabassum Naz Sindhu, Zawar Hussain, Naif Alotaibi, Taseer Muhammad. Estimation method of mixture distribution and modeling of COVID-19 pandemic[J]. AIMS Mathematics, 2022, 7(6): 9926-9956. doi: 10.3934/math.2022554

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Abstract

The mathematical characteristics of the mixture of Lindley model with 2-component (2-CMLM) are discussed. In this paper, we investigate both the practical and theoretical aspects of the 2-CMLM. We investigate several statistical features of the mixed model like probability generating function, cumulants, characteristic function, factorial moment generating function, mean time to failure, Mills Ratio, mean residual life. The density, hazard rate functions, mean, coefficient of variation, skewness, and kurtosis are all shown graphically. Furthermore, we use appropriate approaches such as maximum likelihood, least square and weighted least square methods to estimate the pertinent parameters of the mixture model. We use a simulation study to assess the performance of suggested methods. Eventually, modelling COVID-19 patient data demonstrates the effectiveness and utility of the 2-CMLM. The proposed model outperformed the two component mixture of exponential model as well as two component mixture of Weibull model in practical applications, indicating that it is a good candidate distribution for modelling COVID-19 and other related data sets.

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