A new approach on fractional calculus and probability density function
In statistical analysis, oftentimes a probability density function is used to describe the relationship between certain unknown parameters and measurements taken to learn about them. As soon as there is more than enough data collected to determine a unique solution for the parameters, an estimation...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-09-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020451/fulltext.html |
| _version_ | 1818841902769766400 |
|---|---|
| author | Shu-Bo Chen Saima Rashid Muhammad Aslam Noor Rehana Ashraf Yu-Ming Chu |
| author_facet | Shu-Bo Chen Saima Rashid Muhammad Aslam Noor Rehana Ashraf Yu-Ming Chu |
| author_sort | Shu-Bo Chen |
| collection | DOAJ |
| description | In statistical analysis, oftentimes a probability density function is used to describe the relationship between certain unknown parameters and measurements taken to learn about them. As soon as there is more than enough data collected to determine a unique solution for the parameters, an estimation technique needs to be applied such as “fractional calculus”, for instance, which turns out to be optimal under a wide range of criteria. In this context, we aim to present some novel estimates based on the expectation and variance of a continuous random variable by employing generalized Riemann-Liouville fractional integral operators. Besides, we obtain a two-parameter extension of generalized Riemann-Liouville fractional integral inequalities, and provide several modifications in the Riemann-Liouville and classical sense. Our ideas and obtained results my stimulate further research in statistical analysis. |
| first_indexed | 2024-12-19T04:33:28Z |
| format | Article |
| id | doaj.art-651e1f1a30894f68b9e55bf2b6f3effc |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T04:33:28Z |
| publishDate | 2020-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-651e1f1a30894f68b9e55bf2b6f3effc2022-12-21T20:35:48ZengAIMS PressAIMS Mathematics2473-69882020-09-01567041705410.3934/math.2020451A new approach on fractional calculus and probability density functionShu-Bo Chen0Saima Rashid1Muhammad Aslam Noor2Rehana Ashraf3Yu-Ming Chu41 School of Science, Hunan City University, Yiyang 413000, China2 Department of Mathematics, Government College University, Faisalabad, Pakistan3 Department of Mathematics, COMSATS Universty Islamabad, Isalamabad, Pakistan4 Department of Mathematics, Lahore College for Women Universty, Jhangh Campus, Lahore, Pakistan5 Department of Mathematics, Huzhou University, Huzhou 313000, China 6 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. ChinaIn statistical analysis, oftentimes a probability density function is used to describe the relationship between certain unknown parameters and measurements taken to learn about them. As soon as there is more than enough data collected to determine a unique solution for the parameters, an estimation technique needs to be applied such as “fractional calculus”, for instance, which turns out to be optimal under a wide range of criteria. In this context, we aim to present some novel estimates based on the expectation and variance of a continuous random variable by employing generalized Riemann-Liouville fractional integral operators. Besides, we obtain a two-parameter extension of generalized Riemann-Liouville fractional integral inequalities, and provide several modifications in the Riemann-Liouville and classical sense. Our ideas and obtained results my stimulate further research in statistical analysis.https://www.aimspress.com/article/10.3934/math.2020451/fulltext.htmlgeneralized riemann-liouville fractional integral operatorintegral inequalityexpectationvariance |
| spellingShingle | Shu-Bo Chen Saima Rashid Muhammad Aslam Noor Rehana Ashraf Yu-Ming Chu A new approach on fractional calculus and probability density function AIMS Mathematics generalized riemann-liouville fractional integral operator integral inequality expectation variance |
| title | A new approach on fractional calculus and probability density function |
| title_full | A new approach on fractional calculus and probability density function |
| title_fullStr | A new approach on fractional calculus and probability density function |
| title_full_unstemmed | A new approach on fractional calculus and probability density function |
| title_short | A new approach on fractional calculus and probability density function |
| title_sort | new approach on fractional calculus and probability density function |
| topic | generalized riemann-liouville fractional integral operator integral inequality expectation variance |
| url | https://www.aimspress.com/article/10.3934/math.2020451/fulltext.html |
| work_keys_str_mv | AT shubochen anewapproachonfractionalcalculusandprobabilitydensityfunction AT saimarashid anewapproachonfractionalcalculusandprobabilitydensityfunction AT muhammadaslamnoor anewapproachonfractionalcalculusandprobabilitydensityfunction AT rehanaashraf anewapproachonfractionalcalculusandprobabilitydensityfunction AT yumingchu anewapproachonfractionalcalculusandprobabilitydensityfunction AT shubochen newapproachonfractionalcalculusandprobabilitydensityfunction AT saimarashid newapproachonfractionalcalculusandprobabilitydensityfunction AT muhammadaslamnoor newapproachonfractionalcalculusandprobabilitydensityfunction AT rehanaashraf newapproachonfractionalcalculusandprobabilitydensityfunction AT yumingchu newapproachonfractionalcalculusandprobabilitydensityfunction |