Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data
The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution p...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-11-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/21/4102 |
| _version_ | 1797467386941538304 |
|---|---|
| author | Heba F. Nagy Amer Ibrahim Al-Omari Amal S. Hassan Ghadah A. Alomani |
| author_facet | Heba F. Nagy Amer Ibrahim Al-Omari Amal S. Hassan Ghadah A. Alomani |
| author_sort | Heba F. Nagy |
| collection | DOAJ |
| description | The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution parameters, which is extensively applied in life testing and reliability studies. Some estimation techniques are regarded, including the maximum likelihood, the maximum product of spacing’s, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling. We demonstrate a simulation investigation to assess the performance of the suggested RSS-based estimators via accuracy measures relative to simple random sampling. On the basis of actual data regarding the waiting times between 65 consecutive eruptions of Kiama Blowhole, additional conclusions have been drawn. The outcomes of simulation and real data application demonstrated that RSS-based estimators outperformed their simple random sampling counterparts significantly based on the same number of measured units. |
| first_indexed | 2024-03-09T18:51:54Z |
| format | Article |
| id | doaj.art-718d5a9bfded40d795d0d10935b77106 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:51:54Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-718d5a9bfded40d795d0d10935b771062023-11-24T05:44:56ZengMDPI AGMathematics2227-73902022-11-011021410210.3390/math10214102Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real DataHeba F. Nagy0Amer Ibrahim Al-Omari1Amal S. Hassan2Ghadah A. Alomani3Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, JordanFaculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaThe ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution parameters, which is extensively applied in life testing and reliability studies. Some estimation techniques are regarded, including the maximum likelihood, the maximum product of spacing’s, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling. We demonstrate a simulation investigation to assess the performance of the suggested RSS-based estimators via accuracy measures relative to simple random sampling. On the basis of actual data regarding the waiting times between 65 consecutive eruptions of Kiama Blowhole, additional conclusions have been drawn. The outcomes of simulation and real data application demonstrated that RSS-based estimators outperformed their simple random sampling counterparts significantly based on the same number of measured units.https://www.mdpi.com/2227-7390/10/21/4102ranked set samplinginverted Kumaraswamy distributionmaximum product spacingmaximum likelihoodCramer–von Mises |
| spellingShingle | Heba F. Nagy Amer Ibrahim Al-Omari Amal S. Hassan Ghadah A. Alomani Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data Mathematics ranked set sampling inverted Kumaraswamy distribution maximum product spacing maximum likelihood Cramer–von Mises |
| title | Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data |
| title_full | Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data |
| title_fullStr | Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data |
| title_full_unstemmed | Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data |
| title_short | Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data |
| title_sort | improved estimation of the inverted kumaraswamy distribution parameters based on ranked set sampling with an application to real data |
| topic | ranked set sampling inverted Kumaraswamy distribution maximum product spacing maximum likelihood Cramer–von Mises |
| url | https://www.mdpi.com/2227-7390/10/21/4102 |
| work_keys_str_mv | AT hebafnagy improvedestimationoftheinvertedkumaraswamydistributionparametersbasedonrankedsetsamplingwithanapplicationtorealdata AT ameribrahimalomari improvedestimationoftheinvertedkumaraswamydistributionparametersbasedonrankedsetsamplingwithanapplicationtorealdata AT amalshassan improvedestimationoftheinvertedkumaraswamydistributionparametersbasedonrankedsetsamplingwithanapplicationtorealdata AT ghadahaalomani improvedestimationoftheinvertedkumaraswamydistributionparametersbasedonrankedsetsamplingwithanapplicationtorealdata |