Simulating random variables using moment-generating functions and the saddlepoint approximation

When we are given only a transform such as the moment-generating function of a distribution, it is rare that we can efficiently simulate random variables. Possible approaches such as the inverse transform using numerical inversion of the transform are computationally very expensive. However, the saddlepoint approximation is known to be exact for the Normal, Gamma, and inverse Gaussian distribution and remarkably accurate for a large number of others. We explore the efficient use of the saddlepoint approximation for simulating distributions and provide three examples of the accuracy of these simulations.     

Pricing arithmetic Asian option under a two-factor stochastic volatility model with jumps

This paper presents an efficient Monte Carlo simulation scheme based on the variance reduction methods to evaluate arithmetic average Asian options in the context of the double Heston's stochastic volatility model with jumps. This paper consists of two essential parts. The first part presents a new flexible stochastic volatility model, namely, the double Heston model with jumps. In the second part, by combining two variance reduction procedures via Monte Carlo simulation, we propose an efficient Monte Carlo simulation scheme for pricing arithmetic average Asian options under the double Heston model with jumps. Numerical results illustrate the efficiency of our method.     

Bayesian optimal sequential design for nonparametric regression via inhomogeneous evolutionary MCMC

We develop a novel computational methodology for Bayesian optimal sequential design for nonparametric regression. This computational methodology, that we call inhomogeneous evolutionary Markov chain Monte Carlo, combines ideas of simulated annealing, genetic or evolutionary algorithms, and Markov chain Monte Carlo. Our framework allows optimality criteria with general utility functions and general classes of priors for the underlying regression function. We illustrate the usefulness of our novel methodology with applications to experimental design for nonparametric function estimation using Gaussian process priors and free-knot cubic splines priors.     

Partial unit root and surplus-lag Granger causality testing: A Monte Carlo simulation study

Previous literature has shown that the addition of an untested surplus-lag Granger causality test can provide highly robust to stationary, non stationary, long memory, and structural break processes in the forcing variables. This study extends this approach to the partial unit root framework by simulation. Results show good size and power. Therefore, the surplus-lag approach is also robust to partial unit root processes.     

Stochastic comparisons between extreme order statistics from scale models

Stochastic ordering relations between extreme order statistics from exponential, Weibull and gamma distributions have been studied extensively by many researchers in recent years. In this work, we obtain various ordering results for the comparisons of two extreme order statistics from scale models when one set of scale parameters majorizes the other. The new results obtained here are applied when the baseline distributions are exponentiated Weibull or generalized gamma distributions. In this way, we generalize and extend some results established recently in the literature.     

All pairwise comparisons of exponential location parameters under type i censoring — equal scale parameter case

In this paper, procedures for all pairwise comparisons of location parameters of negative exponential populations are developed when the common scale parameter is known or unknown using large sample distributional approximations of the relevant random variables. The small sample performance of these procedures are then examined using Monte Carlo simulation.     

Bayesian estimation and prediction for Weibull model with progressive censoring

This article presents the statistical inferences on Weibull parameters with the data that are progressively type II censored. The maximum likelihood estimators are derived. For incorporation of previous information with current data, the Bayesian approach is considered. We obtain the Bayes estimators under squared error loss with a bivariate prior distribution, and derive the credible intervals for the parameters of Weibull distribution. Also, the Bayes prediction intervals for future observations are obtained in the one- and two-sample cases. The method is shown to be practical, although a computer program is required for its implementation. A numerical example is presented for illustration and some simulation study are performed.     

Foodborne Exposure to Pesticides and Methylmercury in the United Arab Emirates

As part of a comprehensive environmental health strategic planning project initiated by the government of Abu Dhabi, we assessed potential dietary exposure in the United Arab Emirates (UAE) to methylmercury (in seafood) and pesticides (in fruits and vegetables) above international guideline levels. We present results for the UAE population by age, gender, and body mass index. Our results show very low daily risks of exposure to pesticides in fruits and vegetables at levels exceeding WHO guidelines even under the conservative assumption that no pesticides are removed during washing and food preparation. Thus, exposure to pesticides on fruits and vegetables does not appear to be a major public health concern in the UAE. The chances of exposure to methylmercury in seafood are much higher; our model estimates a mean 1 in 5 daily risk of exceeding the FAO/WHO provisional tolerable weekly intake. However, great caution should be used in interpreting these results, as we analyzed only the risks and not the substantial benefits of fish consumption. In fact, previous studies have demonstrated that exposure to the n‐3 polyunsaturated fatty acids in fish can increase IQ in developing children, and it can substantially decrease the risk in adults of coronary heart disease and stroke. Further research is warranted to compare the risk of Me‐Hg exposure from fish to the nutritional benefits of fish consumption in the UAE and to determine appropriate methods to communicate risk and benefit information to the UAE population.     

Production and changeover control policies of a class of failure prone buffered flow-shops

This article deals with a stochastic optimal control problem for a class of buffered multi-parts flow-shops manufacturing system. The involved machines are subject to random breakdowns and repairs. The flow-shop under consideration is not completely flexible and hence requires setup time and cost in order to switch the production from a part type to another, this changeover is carried on the whole line. Our objective is to find the production plan and the sequence of setups that minimise the cost function, which penalises inventories/backlogs and setups. A continuous dynamic programming formulation of the problem is presented. Then, a numerical scheme is adopted to solve the obtained optimality conditions equations for a two buffered serial machines two parts case. A complete heuristic policy, based on the numerical observations which describe the optimal policies in system states, is developed. It will be shown that the obtained policy is a combination of a KANBAN/CONWIP and a modified hedging corridor policy. Moreover, based on our observations and existent research studies extension to cover more complex flow-shops is henceforth possible. The robustness of such a policy is illustrated through sensitivity analysis.     

A monte carlo evaluation of response surface analysis based on paired-comparison data

The use of the logit transformation on paired-comparison data in the weighted least squares analysis of response surfaces for aesthetic qualities of products is discussed. Monte Carlo simulations are employed to investigate the small sample properties of the estimators and test statistics. A secondary objective of the Monte Carlo simulations is the comparison of two transformation procedures. The simulations are of standard-item paired-compar-ison experiments in which ties are not allowed.