Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

A study of large-bowel volvulus in urban Australia

Background: Large-bowel volvulus is a rare cause of bowel obstruction in the industrialized world. We analyzed the presentation and outcome of 49 patients at the Princess Alexandra Hospital, Brisbane, Australia, who received a diagnosis of colonic volvulus from 1991 to 2001. Methods: A retrospective chart study was carried out. Results: Twenty-nine patients had sigmoid volvulus (59%), 19 patients had cecal volvulus (39%) and 1 patient had a transverse colon volvulus (2%). The diagnosis of sigmoid volvulus was made accurately on plain abdominal radiography or contrast enema in 90% of cases (n = 26), compared with only 42% of cases (n = 8) of cecal volvulus. Twenty-two patients with sigmoid volvulus were treated initially with endoscopic decompression. The success rate was 64% (n = 14). There was a high early recurrence rate of sigmoid volvulus for those treated by endoscopic decompression alone (43%) during a mean period of 32 days. Of the 14 patients with cecal volvulus who were treated with right hemicolectomy, 12 had primary anastomosis and 2 had end ileostomy with mucous fistula formation. There was no anastomotic leak following right hemicolectomy with primary anastomosis, even though 6 of these patients had an ischemic cecum. Conclusions: Endoscopic decompression of the sigmoid volvulus was safe and effective as an initial treatment but has a high early recurrence rate. Any patient who is fit enough to undergo operation should have a definitive procedure during the same admission to avoid recurrence. Cecal volvulus is associated with a higher incidence of gangrene and is treated effectively by right hemicolectomy with or without anastomosis. The need for swift operative intervention is emphasized.

The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.