An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Pharmacokinetics and excretion of gamma-hydroxybutyrate (GHB) in healthy subjects

In Europe and the United States, the recreational use of gamma-hydroxy butyric acid (GHB) at dance clubs and "rave" parties has increased substantially. In addition, GHB is used to assist in the commission of sexual assaults. The aim of this controlled clinical study was to acquire pharmacokinetic profiles, detection times, and excretion rates in human subjects. Eight GHB-naïve volunteers were administered a single 25-mg/kg body weight oral dose of GHB, and plasma, urine, and oral fluid specimens were analyzed by using gas chromatography-mass spectrometry (GC-MS). Liquid-liquid extraction was performed after acid conversion of GHB to gamma-butyrolactone. Limits of quantitation of 0.1 (oral fluid), 0.2 (urine), and 0.5 microg/mL (plasma) could be achieved in the selected ion monitoring mode. GHB plasma peaks of 39.4 +/- 25.2 microg/mL (mean +/- SEM) occurred 20-45 min after administration. The terminal plasma elimination half-life was 30.4 +/- 2.45 min, the distribution volume 52.7 +/- 15.0 L, and the total clearance 1228 +/- 233 microL/min. In oral fluid, GHB could be detected up to 360 min, with peak concentrations of 203 +/- 92.4 microg/mL in the 10-min samples. In urine, 200 +/- 71.8 and 230 +/- 86.3 microg/mL, were the highest GHB levels measured at 30 and 60 min, respectively. Only 1.2 +/- 0.2% of the dose was excreted, resulting in a detection window of 720 min. Common side-effects were confusion, sleepiness, and dizziness; euphoria and change of vital functions were not observed. GHB is extensively metabolized and rapidly eliminated in urine and oral fluid. Consequently, samples should be collected as soon as possible after ingestion.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.