A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process
This study proposes a new one-parameter discrete distribution, called a discrete Bilal distribution. The structural properties of the proposed distributions, including the shape of the probability mass function, mode, moments, skewness, kurtosis, index of dispersion, mean deviation, stress-strength...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2022-08-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/384 |
| _version_ | 1817998403112534016 |
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| author | Emrah Altun M. El-Morshedy M. S. Eliwa |
| author_facet | Emrah Altun M. El-Morshedy M. S. Eliwa |
| author_sort | Emrah Altun |
| collection | DOAJ |
| description |
This study proposes a new one-parameter discrete distribution, called a discrete Bilal distribution. The structural properties of the proposed distributions, including the shape of the probability mass function, mode, moments, skewness, kurtosis, index of dispersion, mean deviation, stress-strength reliability, and order statistics, are derived. These properties are expressed in closed-forms. The maximum likelihood and method of moments estimation methods are considered to estimate the unknown model parameter. An extensive simulation study is carried out to examine the finite sample performance of estimation methods. The usefulness of the proposed model is illustrated in the first-order integer-valued autoregressive process. The empirical importance of the proposed models is proved through three real data applications.
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| first_indexed | 2024-04-14T02:53:02Z |
| format | Article |
| id | doaj.art-eef93b6dfeb748fcbd170e95cb097f36 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:53:02Z |
| publishDate | 2022-08-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-eef93b6dfeb748fcbd170e95cb097f362022-12-22T02:16:14ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712022-08-0120410.57805/revstat.v20i4.384A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive ProcessEmrah Altun 0M. El-Morshedy1M. S. Eliwa 2Bartin UniversityAl-Kharj Prince Sattam bin Abdulaziz UniversitysauMansoura University This study proposes a new one-parameter discrete distribution, called a discrete Bilal distribution. The structural properties of the proposed distributions, including the shape of the probability mass function, mode, moments, skewness, kurtosis, index of dispersion, mean deviation, stress-strength reliability, and order statistics, are derived. These properties are expressed in closed-forms. The maximum likelihood and method of moments estimation methods are considered to estimate the unknown model parameter. An extensive simulation study is carried out to examine the finite sample performance of estimation methods. The usefulness of the proposed model is illustrated in the first-order integer-valued autoregressive process. The empirical importance of the proposed models is proved through three real data applications. https://revstat.ine.pt/index.php/REVSTAT/article/view/384Bilal distributionINAR(1) processMethod of momentsMaximum likelihoodSimulation |
| spellingShingle | Emrah Altun M. El-Morshedy M. S. Eliwa A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process Revstat Statistical Journal Bilal distribution INAR(1) process Method of moments Maximum likelihood Simulation |
| title | A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process |
| title_full | A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process |
| title_fullStr | A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process |
| title_full_unstemmed | A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process |
| title_short | A Study on Discrete Bilal Distribution with Properties and Applications on Integervalued Autoregressive Process |
| title_sort | study on discrete bilal distribution with properties and applications on integervalued autoregressive process |
| topic | Bilal distribution INAR(1) process Method of moments Maximum likelihood Simulation |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/384 |
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