MGFs for Rayleigh Random Variables

Expressions are given for the moment generating functions of the Rayleigh and generalized Rayleigh distributions.

Comments on “TOA Estimation for IR-UWB Systems With Different Transceiver Types”

For original article by I. Guvenc, Z. Sahinoglu and P.V. Orlik, see ibid., vol.54, no.6, p.1876-86, June 2006     

Implicit multigrid schemes for challenging aerodynamic simulations on block-structured grids

In this paper, the use of implicit multigrid smoothers for challenging aerodynamic simulations is explored. The block lower–upper symmetric Gauss–Seidel (LU-SGS) and hybrid Runge–Kutta/LU-SGS schemes are implemented in Bombardier’s multiblock Navier–Stokes solver, FANSC. The schemes are compared to the existing Runge–Kutta and point-Jacobi preconditioned explicit multistage smoothers. Through tests ranging from 2D airfoils to 3D wing-body-engine cases, the computational speed-up and robustness of the implicit schemes are evaluated. It is shown that the implicit smoothers present a computational speed-up of at least two, and are significantly more robust, especially for flow problems involving the “power-on” engine boundary condition.     

Inference for a geometric‐poisson‐Rayleigh distribution under progressive‐stress accelerated life tests based on type‐I progressive hybrid censoring with binomial removals

Based on failures of a parallel‐series system, a new distribution called geometric‐Poisson‐Rayleigh distribution is proposed. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other 6 distributions. The progressive‐stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the geometric‐Poisson‐Rayleigh distribution. It is assumed that the scale parameter of the geometric‐Poisson‐Rayleigh distribution satisfies the inverse power law such that the stress is a nonlinear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type‐I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear‐exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. Some point predictors such as the maximum likelihood, conditional median, best unbiased, and Bayes point predictors for future order statistics are obtained. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed, and numerical computations are performed to compare the performance of the implemented methods of estimation and prediction.     

Influence of hydrology on water quality and trophic state of irrigation reservoirs in Sri Lanka

Many reservoirs provide multiple benefits to people around the world, in addition to primary uses such as irrigation. Thus, reservoir management should address their multiple uses. The water quality of ten irrigation reservoirs in Sri Lanka was examined in the present study with the objective of better understanding the effects of hydrological regimes on reservoir water quality and trophic state. Basic limnological parameters pertinent to the nutrient loads to, and trophic state of, the reservoirs were collected from June 2013 to February 2016. The sampling period was arbitrarily divided into two periods of approximately similar duration (period 1 = June 2013–September 2014; period 2 = October 2014–February 2016) to investigate whether or not there was a seasonal variation in the water quality parameters. Although temporal and spatial variations were observed, most water quality parameters were within the levels acceptable for drinking water standards. The 10 reservoirs were also ordinated by principal component analysis (PCA) on the basis of the water quality parameters of the two sampling periods in a two‐dimensional score plot. Reservoirs in the first principal component (PC1) axis were represented by negative scores attributable to the dissolved oxygen concentration and pH and, to a lesser extent, by electrical conductivity and chlorophyll‐a concentration. Positive scores in PC1 were represented by reservoirs with a score loading attributable to alkalinity, nitrate concentration, Secchi depth, temperature and seston weight and, to a lesser extent, from the total phosphorus concentration. There was a significant negative correlation of PC1 scores with relative reservoir water‐level fluctuation (RRLF; the ratio of mean reservoir water‐level amplitude to mean reservoir depth). Furthermore, Carlson's trophic index also were influenced by RRLF, although not by hydraulic retention time (HRT), indicating allochthonous nutrient inputs into the irrigation reservoirs were mainly governed by RRLF, but not by HRT. Thus, the results of the present study provide useful insights into achieving desirable reservoir water quality through the manipulation of the hydrological regime.     

On the approximations for multinormal integration

The system failure probability in structural reliability analysis involves the computation of multivariate normal integrals. The civil and structural engineering literature has seen the development of several approximation methods for the computation of multivariate normal integrals. However, these developments have been totally unaware of the same in the statistics literature. In this note, a 1-line program from a freely downloadable statistical software is provided for the exact computation of m-dimensional multinormal integrals. It is shown that at least two of the known methods from the civil and structural engineering literature lead to inaccurate results.     

Comment on “A general model for long-tailed network traffic approximation”

The recent paper by Wang et al. (J. Supercomput. 38:155–172, 2006) proposed a Hyper Erlang model for long-tailed network traffic approximation. The paper argued that traditional models such as the Pareto, Weibull and log normal distributions are difficult to apply because of “their complex representations and theoretical properties”. The paper went on to say that the Pareto distribution “does not have analytic Laplace transform, and many other heavy-tailed distributions, such as Weibull and log normal also do not have closed-form Laplace transforms”. In the following, we would like to show that one can actually derive explicit expressions for Laplace transforms of heavy-tailed distributions. The next three sections provide explicit expressions for the Laplace transforms of the Pareto, Weibull and the log-normal distributions. To the best of our knowledge, these are the first known results on Laplace transforms of heavy-tailed distributions.

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Reliability analysis of exponentiated Poisson-exponential constant stress accelerated life test model

Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson–Darling, and Right-tail Anderson–Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.     

A Statistical Analysis of Global Economies Using Time Varying Copulas

Computational Economics - The application of time varying copulas has become popular in recent years. Here, we illustrate an application involving stock indices of ten major economies covering all...