Random inequalities via Riemann-Liouville fractional integration

Abstract

We use the two weighted fractional Chebyshev functional to establish new Riemann-Liouville integral results for the Beta function. We also establish several bounds that estimate the fractional moments for the Beta random variable. Other bounds estimating the fractional harmonic means are also discussed.

Subject Classification: (2010):

• 26D15
• 26A33
• 60E15

Keywords:

• Riemann-Liouville integral
• Integral inequality
• Beta distribution
• Fractional expectation
• Fractional moment