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On the fractional probabilistic Taylor's and mean value theorems

2016

In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…

Generalized Taylor’s formulaMean value theoremSurvival bounded order01 natural sciencesStochastic ordering010104 statistics & probabilityCharacterization of exponential distribution; Fractional calculus; Fractional equilibrium distribution; Generalized Taylor’s formula; Mean value theorem; Survival bounded orderFOS: MathematicsCharacterization of exponential distributionApplied mathematics0101 mathematicsMathematicsComputer Science::Information RetrievalApplied MathematicsProbability (math.PR)010102 general mathematicsProbabilistic logic60E99 26A33 26A24Fractional calculusFractional equilibrium distributionFractional calculusExponential functionDistribution (mathematics)Bounded functionMean value theorem (divided differences)Random variableAnalysisMathematics - Probability
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