Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease
Abstract Among diseases, cancer exhibits the fastest global spread, presenting a substantial challenge for patients, their families, and the communities they belong to. This paper is devoted to modeling such a disease as a special case. A newly proposed distribution called the binomial-discrete Erla...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-38709-2 |
| _version_ | 1797769594351386624 |
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| author | Alaa R. El-Alosey Hussein Eledum |
| author_facet | Alaa R. El-Alosey Hussein Eledum |
| author_sort | Alaa R. El-Alosey |
| collection | DOAJ |
| description | Abstract Among diseases, cancer exhibits the fastest global spread, presenting a substantial challenge for patients, their families, and the communities they belong to. This paper is devoted to modeling such a disease as a special case. A newly proposed distribution called the binomial-discrete Erlang-truncated exponential (BDETE) is introduced. The BDETE is a mixture of binomial distribution with the number of trials (parameter $$n$$ n ) taken after a discrete Erlang-truncated exponential distribution. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, Quantile function, moment generating function, Shannon entropy, order statistics, and stress-strength reliability, are provided. The distribution's parameters are estimated using the maximum likelihood method. Two real-world lifetime count data sets from the cancer disease, both of which are right-skewed and over-dispersed, are fitted using the proposed BDETE distribution to evaluate its efficacy and viability. We expect the findings to become standard works in probability theory and its related fields. |
| first_indexed | 2024-03-12T21:10:18Z |
| format | Article |
| id | doaj.art-b74f90757aed4949a9ad125e136e3948 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-12T21:10:18Z |
| publishDate | 2023-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-b74f90757aed4949a9ad125e136e39482023-07-30T11:12:58ZengNature PortfolioScientific Reports2045-23222023-07-0113111210.1038/s41598-023-38709-2Binomial-discrete Erlang-truncated exponential mixture and its application in cancer diseaseAlaa R. El-Alosey0Hussein Eledum1Department of Mathematics, Faculty of Science, Tanta UniversityDepartment of Statistics, Faculty of Science, University of TabukAbstract Among diseases, cancer exhibits the fastest global spread, presenting a substantial challenge for patients, their families, and the communities they belong to. This paper is devoted to modeling such a disease as a special case. A newly proposed distribution called the binomial-discrete Erlang-truncated exponential (BDETE) is introduced. The BDETE is a mixture of binomial distribution with the number of trials (parameter $$n$$ n ) taken after a discrete Erlang-truncated exponential distribution. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, Quantile function, moment generating function, Shannon entropy, order statistics, and stress-strength reliability, are provided. The distribution's parameters are estimated using the maximum likelihood method. Two real-world lifetime count data sets from the cancer disease, both of which are right-skewed and over-dispersed, are fitted using the proposed BDETE distribution to evaluate its efficacy and viability. We expect the findings to become standard works in probability theory and its related fields.https://doi.org/10.1038/s41598-023-38709-2 |
| spellingShingle | Alaa R. El-Alosey Hussein Eledum Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease Scientific Reports |
| title | Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease |
| title_full | Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease |
| title_fullStr | Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease |
| title_full_unstemmed | Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease |
| title_short | Binomial-discrete Erlang-truncated exponential mixture and its application in cancer disease |
| title_sort | binomial discrete erlang truncated exponential mixture and its application in cancer disease |
| url | https://doi.org/10.1038/s41598-023-38709-2 |
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