Research article

A new approach on fractional calculus and probability density function

  • Received: 30 June 2020 Accepted: 30 August 2020 Published: 09 September 2020
  • MSC : 26A51, 26D10, 26A33

  • 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.

    Citation: Shu-Bo Chen, Saima Rashid, Muhammad Aslam Noor, Rehana Ashraf, Yu-Ming Chu. A new approach on fractional calculus and probability density function[J]. AIMS Mathematics, 2020, 5(6): 7041-7054. doi: 10.3934/math.2020451

    Related Papers:

  • 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.


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