A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data
In this paper, the moment inequalities for some aging distributions are derived based on a mathematical class entitled “<i>a new better than renewal used in Laplace transform order in increasing convex order class</i> (NBRULC)”. The introduced inequalities can be utilized as a new mathem...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-11-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/11/2353 |
| _version_ | 1797466397428678656 |
|---|---|
| author | Mahmoud El-Morshedy Afrah Al-Bossly Rashad M. EL-Sagheer Bader Almohaimeed Waleed B. H. Etman Mohamed S. Eliwa |
| author_facet | Mahmoud El-Morshedy Afrah Al-Bossly Rashad M. EL-Sagheer Bader Almohaimeed Waleed B. H. Etman Mohamed S. Eliwa |
| author_sort | Mahmoud El-Morshedy |
| collection | DOAJ |
| description | In this paper, the moment inequalities for some aging distributions are derived based on a mathematical class entitled “<i>a new better than renewal used in Laplace transform order in increasing convex order class</i> (NBRULC)”. The introduced inequalities can be utilized as a new mathematical test for the exponentiality property versus NBRULC. If the mean life is finitely based on these inequalities, then all higher-order moments exist. Pitman’s asymptotic efficiency of the new mathematical test is derived and studied in detail for some asymmetric probability models. The new mathematical test’s power is estimated in reliability studies for a few well-known alternative asymmetric models. The problem in the case of right-censored data is also handled. After that, applying the suggested test to practical issues is demonstrated using asymmetric, real datasets. |
| first_indexed | 2024-03-09T18:35:24Z |
| format | Article |
| id | doaj.art-9add8b4e585e4d86a7f3a6ceb57db490 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:35:24Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9add8b4e585e4d86a7f3a6ceb57db4902023-11-24T07:08:57ZengMDPI AGSymmetry2073-89942022-11-011411235310.3390/sym14112353A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric DataMahmoud El-Morshedy0Afrah Al-Bossly1Rashad M. EL-Sagheer2Bader Almohaimeed3Waleed B. H. Etman4Mohamed S. Eliwa5Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaMathematics Department, Faculty of Science, Al-Azhar University, Cairo 11884, EgyptDepartment of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi ArabiaFaculty of Computer and Artificial Intelligence, Modern University for Technology and Information, Cairo 12613, EgyptDepartment of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi ArabiaIn this paper, the moment inequalities for some aging distributions are derived based on a mathematical class entitled “<i>a new better than renewal used in Laplace transform order in increasing convex order class</i> (NBRULC)”. The introduced inequalities can be utilized as a new mathematical test for the exponentiality property versus NBRULC. If the mean life is finitely based on these inequalities, then all higher-order moments exist. Pitman’s asymptotic efficiency of the new mathematical test is derived and studied in detail for some asymmetric probability models. The new mathematical test’s power is estimated in reliability studies for a few well-known alternative asymmetric models. The problem in the case of right-censored data is also handled. After that, applying the suggested test to practical issues is demonstrated using asymmetric, real datasets.https://www.mdpi.com/2073-8994/14/11/2353increasing convex ordermoment’s inequalitieshypothesis tests |
| spellingShingle | Mahmoud El-Morshedy Afrah Al-Bossly Rashad M. EL-Sagheer Bader Almohaimeed Waleed B. H. Etman Mohamed S. Eliwa A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data Symmetry increasing convex order moment’s inequalities hypothesis tests |
| title | A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data |
| title_full | A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data |
| title_fullStr | A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data |
| title_full_unstemmed | A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data |
| title_short | A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data |
| title_sort | moment inequality for the nbrulc class statistical properties with applications to model asymmetric data |
| topic | increasing convex order moment’s inequalities hypothesis tests |
| url | https://www.mdpi.com/2073-8994/14/11/2353 |
| work_keys_str_mv | AT mahmoudelmorshedy amomentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT afrahalbossly amomentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT rashadmelsagheer amomentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT baderalmohaimeed amomentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT waleedbhetman amomentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT mohamedseliwa amomentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT mahmoudelmorshedy momentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT afrahalbossly momentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT rashadmelsagheer momentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT baderalmohaimeed momentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT waleedbhetman momentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata AT mohamedseliwa momentinequalityforthenbrulcclassstatisticalpropertieswithapplicationstomodelasymmetricdata |