A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries
The aim of this paper is to introduce a discrete mixture model from the point of view of reliability and ordered statistics theoretically and practically for modeling extreme and outliers' observations. The base distribution can be expressed as a mixture of gamma and Lindley models. A wide rang...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023340?viewType=HTML |
| _version_ | 1811159673293766656 |
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| author | Mohamed S. Eliwa Buthaynah T. Alhumaidan Raghad N. Alqefari |
| author_facet | Mohamed S. Eliwa Buthaynah T. Alhumaidan Raghad N. Alqefari |
| author_sort | Mohamed S. Eliwa |
| collection | DOAJ |
| description | The aim of this paper is to introduce a discrete mixture model from the point of view of reliability and ordered statistics theoretically and practically for modeling extreme and outliers' observations. The base distribution can be expressed as a mixture of gamma and Lindley models. A wide range of the reported model structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, reversed hazard rate function, min-max models, mean residual life, mean past life, moments, order statistics and L-moment statistics. These properties can be formulated as closed forms. It is found that the proposed model can be used effectively to evaluate over- and under-dispersed phenomena. Moreover, it can be applied to analyze asymmetric data under extreme and outliers' notes. To get the competent estimators for modeling observations, the maximum likelihood approach is utilized under conditions of the Newton-Raphson numerical technique. A simulation study is carried out to examine the bias and mean squared error of the estimators. Finally, the flexibility of the discrete mixture model is explained by discussing three COVID-19 data sets. |
| first_indexed | 2024-04-10T05:46:15Z |
| format | Article |
| id | doaj.art-3d7a72f76d8549ca9b9a42ffdd9f25ca |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-10T05:46:15Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-3d7a72f76d8549ca9b9a42ffdd9f25ca2023-03-06T01:36:41ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-02-012057859788110.3934/mbe.2023340A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countriesMohamed S. Eliwa 0Buthaynah T. Alhumaidan 1Raghad N. Alqefari21. Department of Statistics and Operation Research, College of Science, Buraydah 51482, Qassim University, Saudi Arabia 2. Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy 3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt1. Department of Statistics and Operation Research, College of Science, Buraydah 51482, Qassim University, Saudi Arabia1. Department of Statistics and Operation Research, College of Science, Buraydah 51482, Qassim University, Saudi ArabiaThe aim of this paper is to introduce a discrete mixture model from the point of view of reliability and ordered statistics theoretically and practically for modeling extreme and outliers' observations. The base distribution can be expressed as a mixture of gamma and Lindley models. A wide range of the reported model structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, reversed hazard rate function, min-max models, mean residual life, mean past life, moments, order statistics and L-moment statistics. These properties can be formulated as closed forms. It is found that the proposed model can be used effectively to evaluate over- and under-dispersed phenomena. Moreover, it can be applied to analyze asymmetric data under extreme and outliers' notes. To get the competent estimators for modeling observations, the maximum likelihood approach is utilized under conditions of the Newton-Raphson numerical technique. A simulation study is carried out to examine the bias and mean squared error of the estimators. Finally, the flexibility of the discrete mixture model is explained by discussing three COVID-19 data sets.https://www.aimspress.com/article/doi/10.3934/mbe.2023340?viewType=HTMLmixed distributionsdiscretization techniquefailure analysissimulationcovid-19statistics and numerical data |
| spellingShingle | Mohamed S. Eliwa Buthaynah T. Alhumaidan Raghad N. Alqefari A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries Mathematical Biosciences and Engineering mixed distributions discretization technique failure analysis simulation covid-19 statistics and numerical data |
| title | A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries |
| title_full | A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries |
| title_fullStr | A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries |
| title_full_unstemmed | A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries |
| title_short | A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries |
| title_sort | discrete mixed distribution statistical and reliability properties with applications to model covid 19 data in various countries |
| topic | mixed distributions discretization technique failure analysis simulation covid-19 statistics and numerical data |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023340?viewType=HTML |
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