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A rejection algorithm { called transformed density rejection { that uses a new method for constructing simple hat functions for an unimodal, bounded density f is introduced. It is based on the idea to transform f with a suitable transformation T such that T (f(x)) is concave. f is then called T-concave and tangents of T (f(x)) in the mode and in a point on… (More)

We give an algorithm that can be used to sample from any discrete log-concave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast for all discrete log-concave distributions and not much slower… (More)

A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept through the given polytope until a random fraction (sampled from a proper univariate distribution) of the volume of the polytope is covered. Then the intersection of the plane with the… (More)

Different automatic (also called universal or black-box) methods have been suggested to sample from univariate log-concave distributions. Our new automatic algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is… (More)

The inversion method for generating nonuniform random variates has some advantages compared to other generation methods, since it monotonically transforms uniform random numbers into non-uniform random variates. Hence, it is the method of choice in the simulation literature. However, except for some simple cases where the inverse of the cumulative… (More)

We present a numerical inversion method for generating random variates from continuous distributions when only the density function is given. The algorithm is based on polynomial interpolation of the inverse CDF and Gauss-Lobatto integration. The user can select the required precision, which may be close to machine precision for smooth, bounded densities;… (More)

For discrete distributions a variant of reject from a continuous hat function is presented. The main advantage of the new method, called <italic>rejection-inversion</italic>, is that no extra uniform random number to decide between acceptance and rejection is required, which means that the expected number of uniform variates required is halved. Using… (More)

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads… (More)

We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There… (More)