Simulation techniques for generalized Gaussian densities

This contribution deals with the Monte Carlo simulation of generalized Gaussian random variables. Such a parametric family of distributions has been proposed in many applications in science to describe physical phenomena and in engineering, and it seems to be also useful in modelling economic and financial data. For values of the shape parameter α within a certain range, the distribution presents heavy tails. In particular, the cases α=1/3 and α=1/2 are considered. For such values of the shape parameter, different simulation methods are assessed.     

A Hellinger distance approach to MCMC diagnostics

Bayesian analysis often requires the researcher to employ Markov Chain Monte Carlo (MCMC) techniques to draw samples from a posterior distribution which in turn is used to make inferences. Currently, several approaches to determine convergence of the chain as well as sensitivities of the resulting inferences have been developed. This work develops a Hellinger distance approach to MCMC diagnostics. An approximation to the Hellinger distance between two distributions f and g based on sampling is introduced. This approximation is studied via simulation to determine the accuracy. A criterion for using this Hellinger distance for determining chain convergence is proposed as well as a criterion for sensitivity studies. These criteria are illustrated using a dataset concerning the Anguilla australis, an eel native to New Zealand.     

Rank invariant tests with left truncated and interval censored data

Peto and Peto (1972) have studied rank invariant tests to compare two survival curves for right censored data. We apply their tests, including the logrank test and the generalized Wilcoxon test, to left truncated and interval censored data. The significance levels of the tests are approximated by Monte Carlo permutation tests. Simulation studies are conducted to show their size and power under different distributional differences. In particular, the logrank test works well under the Cox proportional hazards alternatives, as for the usual right censored data. The methods are illustrated by the analysis of the Massachusetts Health Care Panel Study dataset.     

Latin hypercube sampling with multidimensional uniformity

Complex models can only be realized a limited number of times due to large computational requirements. Methods exist for generating input parameters for model realizations including Monte Carlo simulation (MCS) and Latin hypercube sampling (LHS). Recent algorithms such as maximinLHS seek to maximize the minimum distance between model inputs in the multivariate space. A novel extension of Latin hypercube sampling (LHSMDU) for multivariate models is developed here that increases the multidimensional uniformity of the input parameters through sequential realization elimination. Correlations are considered in the LHSMDU sampling matrix using a Cholesky decomposition of the correlation matrix. Computer code implementing the proposed algorithm supplements this article. A simulation study comparing MCS, LHS, maximinLHS and LHSMDU demonstrates that increased multidimensional uniformity can significantly improve realization efficiency and that LHSMDU is effective for large multivariate problems.     

Monte carlo estimates of the distributions of the random polygons of the voronoi tessellation with respect to a poisson process

A large-scale study, in which two million random Voronoi polygons (with respect to a homogeneous Poisson point process) were generated and mensurated, is described. The polygon characteristics recorded are number of sides (or vertices), perimeter, area and interior angles. A feature is the efficient “quantile” method of replicating Poisson-type random structures, which it is hoped may find useful application elsewhere.     

Exact monte carlo tests using several statistics

Concepts of ranking and boundary of multivariate statistics are discussed and applied to the simultaneous use of several test statistics calculated for data and simulated replicates. An example of residual analysis in regression is given using layer ranks and supplementary simulation with a stopping rule.     

Monte Carlo comparison of five exponentiality tests using different entropy estimates

The paper studies five entropy tests of exponentiality using five statistics based on different entropy estimates. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for each of the test statistics. By simulation, we compare the power of these five tests for various alternatives and sample sizes.     

An adaptive two-sample location-scale test of lepage type for symmetric distributions

For the two-sample location and scale problem we propose an adaptive test which is based on so called Lepage type tests. The well known test of Lepage (1971) is a combination of the Wilcoxon test for location alternatives and the Ansari-Bradley test for scale alternatives and it behaves well for symmetric and medium-tailed distributions. For the cae of short-, medium- and long-tailed distributions we replace the Wilcoxon test and the .Ansari-Bradley test by suitable other two-sample tests for location and scale, respectively, in oder to get higher power than the classical Lepage test for such distribotions. These tests here are called Lepage type tests. in practice, however, we generally have no clear idea about the distribution having generated our data. Thus, an adaptive test should be applied which takes the the given data set inio consideration. The proposed adaptive test is based on the concept of Hogg (1974), i.e., first, to classify the unknown symmetric distribution function with respect to a measure for tailweight and second, to apply an appropriate Lepage type test for this classified type of distribution. We compare the adaptive test with the three Lepage type tests in the adaptive scheme and with the classical Lepage test as well as with other parametric and nonparametric tests. The power comparison is carried out via Monte Carlo simulation. It is shown that the adaptive test is the best one for the broad class of distributions considered.     

Earthquakes occurrences estimation through a parametric semi-Markov approach

The estimation of earthquakes’ occurrences prediction in seismic areas is a challenging problem in seismology and earthquake engineering. Indeed, the prevention and the quantification of possible damage provoked by destructive earthquakes are directly linked to this kind of prevision. In our paper, we adopt a parametric semi-Markov approach. This model assumes that a sequence of earthquakes is seen as a Markov process and besides it permits to take into consideration the more realistic assumption of events’ dependence in space and time. The elapsed time between two consecutive events is modeled as a general Weibull distribution. We determine then the transition probabilities and the so-called crossing states probabilities. We conclude then with a Monte Carlo simulation and the model is validated through a large database containing real data.     

C14. Moments of the kolmogorov-smirnov one-sample statistic

In adaptive estimation, it is often considered that an estimator has made a mistake if the component estimator chosen for use is not the most efficient for the distribution sampled. Theoretical and simulation results point to a fallacy in this line of thought. The Monte Carlo study involves extension of the Princeton Swindle to distributions conditional on a location and scale-free statistic, and to the uniform. The results give a partial explanation for the sometimes surprising robustness of adaptive L-estimators.