Maximum Entropy Density Estimation from Fractional Moments

Abstract

A procedure for the estimation of probability density functions of positive random variables by its fractional moments, is presented. When all the available information is provided by population fractional moments a criterion of choosing fractional moments themselves is detected. When only a sample is known, Jaynes' maximum entropy procedure and the Akaike's estimation procedure are joined together for determining respectively, what and how many sample fractional moments have to be used in the estimation of the density. Some numerical experiments are provided.

Entropy and density approximation from Laplace transforms

“…. , M for some a > 0, are selected, Novi-Inverardi and Tagliani [16] proved f M converge in entropy to the underlying unknown density f Y . As a consequence, entropy convergence is guaranteed and accelerated when nodes α j = ja/M are replaced by optimal nodes obtained in (4.5).…”

An Unbiased Method for Probabilistic Fire Safety Engineering, Requiring a Limited Number of Model Evaluations

“…As shown by Novi Inverardi and Tagliani (2003), this principle results in an estimated PDF given by equation (5), with m the estimation order, λi estimated coefficients and αi estimated exponents. The coefficient λ0 normalizes the PDF -i.e.…”

“…In principle the estimation order m can be freely chosen, but while a higher estimation order will result in a better agreement with the input data, a too high estimation order may introduce spurious relationships for (unavoidably) limited sets of input data y j. Novi Inverardi and Tagliani (2003) propose to evaluate the ME optimization of (5)- (7) for different m, and choose the result for which the value of (7) is minimal while taking into account a penalty factor for increased m. For the applications further in this paper, this procedure however does not result in a clear preference for m as the resulting minimized values are very close to each other, resulting in a preference which may at times depend on the starting solution or optimization algorithm. This will be further investigated in follow-up research.…”

Efficient option valuation of single and double barrier options

“…Since we want to think of Mellin transform as fractional moments [12], we will modify definitions a bit and say that a function…”