Alternatively, A random variate with a given non-uniform distribution can often by generated in one assignment statement if a uniform source and some simple functions are available. We review such one-line methods for most of the key distributions. 1 A MODEL OF COMPUTATION Random variate generators that are conceptually simple and quick to program become invariably popular, even if they are not...

The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of intersest and the control variable are i.i.d. Here we assume that these v...

We prove that any multi-variate Hasse-Schmidt derivation can be decomposed in terms of substitution maps and uni-variate derivations. As a consequence we the bracket two $m$-integrable derivations is also $m$-integrable, for $m$ positive integer or infinity.

In this paper, we determine the symmetrised density of a nonsingular doubly noncentral matrix variate beta type I and II distributions under different definitions.

Both canonical correlation analysis (CCA) and principal component analysis (PCA) were applied to atmospheric aerosol and trace gas concentrations and meteorological data collected in Chicago during the summer months of 2002, 2003, and 2004. Concentrations of ammonium, calcium, nitrate, sulfate, and oxalate particulate matter, as well as, meteorological parameters temperature, wind speed, wind d...

The conventional control variate method proposed by Kemna and Vorst (1990) to evaluate Asian options under the Black-Scholes model can be interpreted as a particular selection of linear martingale controls. We generalize the constant control parameter into a control process to gain more reduction on variance. By means of an option price approximation, we construct a martingale control variate m...

We examine the directional predictability of energy stock returns on exchange rates and market in E7 + 1 emerging economies, which include India, China, Indonesia, South Korea, Turkey, Brazil, Mexico, Russia, over period 4 January 2000 to 31 May 2018. To achieve this, we carried out a cross-quantile analysis static dynamic frameworks, using bi-variate cross-quantilogram (CQ) partial (PCQ) appro...