Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications
Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/2219570 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547142666813440 |
|---|---|
| author | Farwa Willayat Naz Saud Muhammad Ijaz Anita Silvianita Mahmoud El-Morshedy |
| author_facet | Farwa Willayat Naz Saud Muhammad Ijaz Anita Silvianita Mahmoud El-Morshedy |
| author_sort | Farwa Willayat |
| collection | DOAJ |
| description | Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J-shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT-II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT-II distribution have been shown using three real life data sets. The MOEGT-II distribution has been demonstrated as better fit than Exponentiated Gumbel Type-II (EGT-II), Marshall–Olkin Gumbel Type-II (MOGT-II), Gumbel Type-II (GT-II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions. |
| format | Article |
| id | doaj-art-439327577f414562aea3129feced7821 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-439327577f414562aea3129feced78212025-02-03T06:45:55ZengWileyComplexity1099-05262022-01-01202210.1155/2022/2219570Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and ApplicationsFarwa Willayat0Naz Saud1Muhammad Ijaz2Anita Silvianita3Mahmoud El-Morshedy4Department of StatisticsDepartment of StatisticsDepartment of Mathematics and StatisticsSchool of communications and businessDepartment of Mathematics, College of Sciences and Humanities in Al-KharjDue to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J-shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT-II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT-II distribution have been shown using three real life data sets. The MOEGT-II distribution has been demonstrated as better fit than Exponentiated Gumbel Type-II (EGT-II), Marshall–Olkin Gumbel Type-II (MOGT-II), Gumbel Type-II (GT-II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions.http://dx.doi.org/10.1155/2022/2219570 |
| spellingShingle | Farwa Willayat Naz Saud Muhammad Ijaz Anita Silvianita Mahmoud El-Morshedy Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications Complexity |
| title | Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications |
| title_full | Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications |
| title_fullStr | Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications |
| title_full_unstemmed | Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications |
| title_short | Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications |
| title_sort | marshall olkin extended gumbel type ii distribution properties and applications |
| url | http://dx.doi.org/10.1155/2022/2219570 |
| work_keys_str_mv | AT farwawillayat marshallolkinextendedgumbeltypeiidistributionpropertiesandapplications AT nazsaud marshallolkinextendedgumbeltypeiidistributionpropertiesandapplications AT muhammadijaz marshallolkinextendedgumbeltypeiidistributionpropertiesandapplications AT anitasilvianita marshallolkinextendedgumbeltypeiidistributionpropertiesandapplications AT mahmoudelmorshedy marshallolkinextendedgumbeltypeiidistributionpropertiesandapplications |