Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset
The Exponential Pareto (EP) model has been extended by applied and theoretical statisticians for wider applications and new knowledge using different techniques but the Weibull-X technique has not been considered. This article proposed a new extension of the EP model called the Weibull-Exponential P...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Magister Program of Material Sciences, Graduate School of Universitas Sriwijaya
2023-04-01
|
| Series: | Science and Technology Indonesia |
| Subjects: | |
| Online Access: | https://sciencetechindonesia.com/index.php/jsti/article/view/624/314 |
| _version_ | 1797283564237094912 |
|---|---|
| author | Adewunmi Olaniran Adeyemi Ismail Adedeji Adeleke Eno Emmanuella Akarawak |
| author_facet | Adewunmi Olaniran Adeyemi Ismail Adedeji Adeleke Eno Emmanuella Akarawak |
| author_sort | Adewunmi Olaniran Adeyemi |
| collection | DOAJ |
| description | The Exponential Pareto (EP) model has been extended by applied and theoretical statisticians for wider applications and new knowledge using different techniques but the Weibull-X technique has not been considered. This article proposed a new extension of the EP model called the Weibull-Exponential Pareto (WEP) distribution to provide better modeling that fits real-life datasets and to explore the statistical theory of order statistics from the proposed distribution. Statistical properties investigated include the Shannon and Renyi entropies; the moments and moment generating function. Distribution of order statistics and the moment of order statistics were derived including the mean and variance of order statistics. WEP distribution has unimodal, decreasing, and increasing failure rates; and it can be negatively or positively skewed and approximately symmetric with the potential for fitting platykurtic, mesokurtic, and leptokurtic lifetime data. The parameters of the distribution were estimated using the method of maximum likelihood estimation (MLE), which was examined for consistency through a simulation study. The performance of the proposed distribution was investigated by application to flood peaks exceedances and some lifetime datasets from engineering. The results from data analysis using the R-software revealed that the WEP distribution has the potential to provide a superior model that fits the three data sets better than some notable existing distributions and previous extensions of the EP model in the literature. The statistical property of order statistics extended in the study established some important results that characterized some notable lifetime distributions in the literature. |
| first_indexed | 2024-03-07T17:32:32Z |
| format | Article |
| id | doaj.art-f4b17817bfda47e4bed9efdf3ee24086 |
| institution | Directory Open Access Journal |
| issn | 2580-4405 2580-4391 |
| language | English |
| last_indexed | 2024-03-07T17:32:32Z |
| publishDate | 2023-04-01 |
| publisher | Magister Program of Material Sciences, Graduate School of Universitas Sriwijaya |
| record_format | Article |
| series | Science and Technology Indonesia |
| spelling | doaj.art-f4b17817bfda47e4bed9efdf3ee240862024-03-02T17:36:33ZengMagister Program of Material Sciences, Graduate School of Universitas SriwijayaScience and Technology Indonesia2580-44052580-43912023-04-018226527910.26554/sti.2023.8.2.265-279Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime DatasetAdewunmi Olaniran Adeyemi0Ismail Adedeji Adeleke1Eno Emmanuella Akarawak2Department of Statistics, Faculty of Science, University of Lagos, Lagos, 101017, NigeriaDepartment of Actuarial Science and Insurance, University of Lagos, Lagos, 101017, NigeriaDepartment of Statistics, Faculty of Science, University of Lagos, Lagos, 101017, NigeriaThe Exponential Pareto (EP) model has been extended by applied and theoretical statisticians for wider applications and new knowledge using different techniques but the Weibull-X technique has not been considered. This article proposed a new extension of the EP model called the Weibull-Exponential Pareto (WEP) distribution to provide better modeling that fits real-life datasets and to explore the statistical theory of order statistics from the proposed distribution. Statistical properties investigated include the Shannon and Renyi entropies; the moments and moment generating function. Distribution of order statistics and the moment of order statistics were derived including the mean and variance of order statistics. WEP distribution has unimodal, decreasing, and increasing failure rates; and it can be negatively or positively skewed and approximately symmetric with the potential for fitting platykurtic, mesokurtic, and leptokurtic lifetime data. The parameters of the distribution were estimated using the method of maximum likelihood estimation (MLE), which was examined for consistency through a simulation study. The performance of the proposed distribution was investigated by application to flood peaks exceedances and some lifetime datasets from engineering. The results from data analysis using the R-software revealed that the WEP distribution has the potential to provide a superior model that fits the three data sets better than some notable existing distributions and previous extensions of the EP model in the literature. The statistical property of order statistics extended in the study established some important results that characterized some notable lifetime distributions in the literature.https://sciencetechindonesia.com/index.php/jsti/article/view/624/314exponential pareto modelweibull-x techniqueweibull-exponential pareto distributionshannon and renyi entropiesdistribution of order statisticsmoment of order statistics |
| spellingShingle | Adewunmi Olaniran Adeyemi Ismail Adedeji Adeleke Eno Emmanuella Akarawak Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset Science and Technology Indonesia exponential pareto model weibull-x technique weibull-exponential pareto distribution shannon and renyi entropies distribution of order statistics moment of order statistics |
| title | Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset |
| title_full | Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset |
| title_fullStr | Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset |
| title_full_unstemmed | Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset |
| title_short | Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset |
| title_sort | extension of exponential pareto distribution with the order statistics some properties and application to lifetime dataset |
| topic | exponential pareto model weibull-x technique weibull-exponential pareto distribution shannon and renyi entropies distribution of order statistics moment of order statistics |
| url | https://sciencetechindonesia.com/index.php/jsti/article/view/624/314 |
| work_keys_str_mv | AT adewunmiolaniranadeyemi extensionofexponentialparetodistributionwiththeorderstatisticssomepropertiesandapplicationtolifetimedataset AT ismailadedejiadeleke extensionofexponentialparetodistributionwiththeorderstatisticssomepropertiesandapplicationtolifetimedataset AT enoemmanuellaakarawak extensionofexponentialparetodistributionwiththeorderstatisticssomepropertiesandapplicationtolifetimedataset |