Formulae for absolute moments

Formulae for Askey-wilson Moments and Enumeration of Staircase Tableaux

We explain how the moments of the (weight function of the) Askey Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors [11, 12]. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the formula given in [11]. Then we use techniques developed by Ismail and the third author to gi...

Moments and Absolute Moments of the Normal Distribution

We present formulas for the (raw and central) moments and absolute moments of the normal distribution. We note that these results are not new, yet many textbooks miss out on at least some of them. Hence, we believe that it is worthwhile to collect these formulas and their derivations in these notes.

Absolute Fourth Moments and Finiteness Of Linear Groups

Small-Time Asymptotics of Option Prices and First Absolute Moments

We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process S follows a general martingale. This is equivalent to studying the first centered absolute moment of S. We show that if S has a continuous part, the leading term is of order √ T in time T and depends only on the initial value of the volatility. Furthermore, the term is linear ...

Blind Separation Using Absolute Moments Based Adaptive Estimating Function

We propose new absolute moment based estimating functions for blind source separation purposes. Absolute moments are a computationally simple choice that can also adapt to the skewness of source distributions. They have lower sample variance than cumulants employed in many widely used ICA (Independent Component Analysis) methods. The complete estimating function consists of two parts that are s...