Methods for generating variates from probability distributions

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Diverse probabilistic results are used in the design of random univariate generators. General methods based on these are classified and relevant theoretical properties derived. This is followed by a comparative review of specific algorithms currently available for continuous and discrete univariate distributions. A need for a Zeta generator is established, and two new methods, based on inversion and rejection with a truncated Pareto envelope respectively are developed and compared. The paucity of algorithms for multivariate generation motivates a classification of general methods, and in particular, a new method involving envelope rejection with a novel target distribution is proposed. A new method for generating first passage times in a Wiener Process is constructed. This is based on the ratio of two random numbers, and its performance is compared to an existing method for generating inverse Gaussian variates. New "hybrid" algorithms for Poisson and Negative Binomial distributions are constructed, using an Alias implementation, together with a Geometric tail procedure. These are shown to be robust, exact and fast for a wide range of parameter values. Significant modifications are made to Atkinson's Poisson generator (PA), and the resulting algorithm shown to be complementary to the hybrid method. A new method for Von Mises generation via a comparison of random numbers follows, and its performance compared to that of Best and Fisher's Wrapped Cauchy rejection method. Finally new methods are proposed for sampling from distribution tails, using optimally designed Exponential envelopes. Timings are given for Gamma and Normal tails, and in the latter case the performance is shown to be significantly better than Marsaglia's tail generation procedure.Governors of Dundee College of Technolog

A review of multi-component maintenance models with economic dependence

In this paper we review the literature on multi-component maintenance models with economic dependence. The emphasis is on papers that appeared after 1991, but there is an overlap with Section 2 of the most recent review paper by Cho and Parlar (1991). We distinguish between stationary models, where a long-term stable situation is assumed, and dynamic models, which can take information into account that becomes available only on the short term. Within the stationary models we choose a classification scheme that is primarily based on the various options of grouping maintenance activities: grouping either corrective or preventive maintenance, or combining preventive-maintenance actions with corrective actions. As such, this classification links up with the possibilities for grouped maintenance activities that exist in practice

The scale and dynamics of COVID-19 epidemics across Europe

The number of COVID-19 deaths reported from European countries has varied more than 100-fold. In terms of coronavirus transmission, the relatively low death rates in some countries could be due to low intrinsic (e.g. low population density) or imposed contact rates (e.g. non-pharmaceutical interventions) among individuals, or because fewer people were exposed or susceptible to infection (e.g. smaller populations). Here, we develop a flexible empirical model (skew-logistic) to distinguish among these possibilities. We find that countries reporting fewer deaths did not generally have intrinsically lower rates of transmission and epidemic growth, and flatter epidemic curves. Rather, countries with fewer deaths locked down earlier, had shorter epidemics that peaked sooner and smaller populations. Consequently, as lockdowns were eased, we expected, and duly observed, a resurgence of COVID-19 across Europe

Sampling From Discrete And Continuous Distributions With C-Rand

C--RAND is a system of Turbo--C routines and functions intended for use on microcomputers. It contains up--to--date random number generators for more than thirty univariate distributions. For some important distributions the user has the choice between extremely fast but rather complicated methods and somewhat slower but also much simpler procedures. Menu driven demo programs allow to test and analyze the generators with regard to speed and quality of the output. 1