This paper demonstrates that basic statistics (mean, variance) of the logarithm of the variate itself can be used in the calculation of differential entropy among random variables known to be multiples and powers of a common underlying variate. For the same set of distributions, the variance of the differential self-information is shown also to be a function of statistics of the logarithmic var...

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on equivalent Black–Scholes (BS) volatility, we instead derive constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces approximation error in a way similar to control variate method because CEV model is zero vol-of-vol limit SABR Moreover, ...

For the usual st raight·line model, in whic h the independent variable ta kes on a fixed, kno wn se t of va lues, it is shown that the sample corre lation coeffi cie nt is distributed as Q with (n-2) degrees of freedom and noncentralit y O=({3 /CT) V~(Xi X)2. The Q variate has been defin ed and studied e lse· where by Hogben et al. It is noted that the square of the correlation coeffi cient is ...

Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted hypergeometric type distributions is also derived as a...

We study training and generalization for multi-variate time series processing. It is suggested to used a quasi maximum likelihood approach rather than the standard sum of squared errors, thus taking dependencies among the errors of the individual time series into account. This may lead to improved generalization performance. Further, we extend the Optimal Brain Damage pruning technique to the m...

We study training and generalization for multi-variate time series processing. It is suggested to used a quasi maximum likelihood approach rather than the standard sum of squared errors, thus taking dependencies among the errors of the individual time series into account. This may lead to improved generalization performance. Further, we extend the Optimal Brain Damage pruning technique to the m...

Quasi-Monte Carlo (QMC) methods have begun to displace ordinary Monte Carlo (MC) methods in many practical problems. It is natural and obvious to combine QMC methods with traditional variance reduction techniques used in MC sampling, such as control variates. There can, however, be some surprises. The optimal control variate coefficient for QMC methods is not in general the same as for MC. Usin...