Further results and applications on continuous random variables
Downloads
DOI:
https://doi.org/10.26637/MJM0703/0011Abstract
New results and new applications of fractional calculus for continuous random variables are presented. New expectation and variance identities of order α ≥1 are established. Under a new fractional normalisation technique, other weighted random variable inequalities are generated and some classical results are deduced as special cases.
Keywords:
Integral inequalities, Riemann-Liouville integral, random variable, fractional expectation, fractional variance, fractional momentMathematics Subject Classification:
Mathematics- Pages: 429-435
- Date Published: 01-07-2019
- Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)
T. Cacoullos and V. Papathanasiou: On upper bounds for the variance of functions of random varialbes, Statist. Probab. Lett., 7 (1985), pp. 175-184.
T. Cacoullos and V. Papathanasiou: Caracterizations of distributuons by variance bounds. Math. Statist., 4 (1989), pp. 351-356.
T. Cacoullos and V. Papathanasiou: Characterizations of distributions by generalisations of variance bounds and simple proofs of the CLT, J. Statist. Plann. Inference, 63 (1997), pp. 157-171.
Z. Dahmani, A.E. Bouziane, M. Houas and M.Z. Sarikaya: New w-weighted concepts for continuous random variables with applications, Note di Matematica, 37(1) (2017), pp. 23-40.
Z. Dahmani: New applications of fractional calculus on probabilistic random variables, Acta Math. Univ. ComenianaeVol. LXXXVI, 2 (2017), pp. 299-307.
F. Goodarzi, M. Amini and G.R. Mohtashami Borzadaran: On upper bounds for the variance of functions of random variables with weighted distributions, Labachevskii Journal of Mathematics, 37(4) (2016), pp. 422-435.
R. Gorenflo, F. Mainardi: Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien, (1997), pp. 223-276.
G.R. Mohtashami Borzadaran and D.N. Shanbhag: Statist. Probab. Lett., 39 (1998), pp. 109-117.
M.Z. Sarikaya, M.E. Kiris,N. Celik: Hermite-Hadamard type inequality for h-convex stochastic processes. AIP Conference Proceedings 1726, 020076 (2016).
M.Z. Sarikaya, T. Tunc, H. Budak: Simpson's type inequality for F-convex function. FACTA Univ. FUMI, 1(10), (2018), pp. 747-753.
M.Z. Sarikaya, H. Yildiz, H. Budak: On weighted Iyengar-type inequalities for conformable fractional integrals. Mathematical Sciences, 11(4), (2017), pp. 327-331.
- NA
Similar Articles
- S. K. Vaidya, A. D. Parmar, On chromatic transversal domination in graphs , Malaya Journal of Matematik: Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
