An R Implementation of the Polya-Aeppli Distribution

An efficient implementation of the Polya-Aeppli, or geometirc compound Poisson, distribution in the statistical programming language R is presented. The implementation is available as the package polyaAeppli and consists of functions for the mass function, cumulative distribution function, quantile function and random variate generation with those parameters conventionally provided for standard univatiate probability distributions in the stats package in RComment: 9 pages, 2 figure

Efficient Programmable Random Variate Generation Accelerator from Sensor Noise

We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo integration of a univariate Gaussian by 1068 times while doubling the speed of the Monte Carlo simulation. We show that the supply voltage and temperature of the physical process must be controlled to prevent the mean and standard deviation of the random number generator from drifting.Alan Turing Institute award: TU/B/000096 EPSRC grants: EP/N510129/1, EP/R022534/1, EP/V004654/1 and EP/L015889/

Class library ranlip for multivariate nonuniform random variate generation

This paper describes generation of nonuniform random variates from Lipschitz-continuous densities using acceptance/rejection, and the class library ranlip which implements this method. It is assumed that the required distribution has Lipschitz-continuous density, which is either given analytically or as a black box. The algorithm builds a piecewise constant upper approximation to the density (the hat function), using a large number of its values and subdivision of the domain into hyperrectangles. The class library ranlip provides very competitive preprocessing and generation times, and yields small rejection constant, which is a measure of efficiency of the generation step. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions. It will be valuable for researchers who frequently face the task of sampling from unusual distributions, for which specialized random variate generators are not available.<br /

Random variate generation for exponential and gamma tilted stable distributions

We develop a new efficient simulation scheme for sampling two families of tilted stable distributions: exponential tilted stable (ETS) and gamma tilted stable (GTS) distributions. Our scheme is based on two-dimensional single rejection. For the ETS family, its complexity is uniformly bounded over all ranges of parameters. This new algorithm outperforms all existing schemes. In particular, it is more efficient than the well-known double rejection scheme, which is the only algorithm with uniformly bounded complexity that we can find in the current literature. Beside the ETS family, our scheme is also flexible to be further extended for generating the GTS family, which cannot easily be done by extending the double rejection scheme. Our algorithms are straightforward to implement, and numerical experiments and tests are conducted to demonstrate the accuracy and efficiency

Some Results Regarding the Estimation of Densities and Random Variate Generation Using Neural Networks

In this paper we consider two important topics: density estimation and random variate generation. We will present a framework that is easily implemented using the familiar multilayer neural network. First, we develop two new methods for density estimation, a stochastic method and a related deterministic method. Both methods are based on approximating the distribution function, the density being obtained by differentiation. In the second part of the paper, we develop new random number generation methods. Our methods do not suffer from some of the restrictions of existing methods in that they can be used to generate numbers from an observed inverse relationship between the density estimation process and the random number generation process. We present two variants of this method -- a stochastic and a deterministic version. We propose a second method that is based on formulating the task as a control problem, where a "controller network" is trained to shape a given density into the desired density. We justify the use of all the methods that we propose by providing theoretical convergence results. In particular, we prove that the L8 convergence to the true density to both the density estimation and random variate generation techniques occurs as a rate O((log log N/N)^((1-e)/2) where N is the number of data points and e can be made arbitrarily small for sufficiently smooth target densities. This bound is very close to the optimally achievable convergence rate under similar smoothness conditions. Also, for comparison, the L2 (RMS) convergence rate of a positive kernel density estimator is O(N^(-2/5)) when the optimal kernel width is used. We present numerical simulations to illustrate the performance of the proposed density estimation and random variate generation methods. In addition, we present an extended introduction and bibliography that serves as an overview and reference for the practitioner

RAGE: A Java-implemented Visual Random Generator

Carefully designed Java applications turn out to be efficient and platform independent tools that can compete well with classical implementations of statistical software. The project presented here is an example underlining this statement for random variate generation. An end-user application called RAGE (Random Variate Generator) is developed to generate random variates from probability distributions. A Java class library called JDiscreteLib has been designed and implemented for the simulation of random variables from the most usual discrete distributions inside RAGE. For each distribution, specific and general algorithms are available for this purpose. RAGE can also be used as an interactive simulation tool for data and data summary visualization.

Random variate generation and connected computational issues for the Poisson–Tweedie distribution

After providing a systematic outline of the stochastic genesis of the Poisson–Tweedie distribution, some computational issues are considered. More specifically, we introduce a closed form for the probability function, as well as its corresponding integral representation which may be useful for large argument values. Several algorithms for generating Poisson–Tweedie random variates are also suggested. Finally, count data connected to the citation profiles of two statistical journals are modeled and analyzed by means of the Poisson–Tweedie distribution

Copulas Related to Manneville-Pomeau Processes

In this work we derive the copulas related to Manneville-Pomeau processes. We examine both bidimensional and multidimensional cases and derive some properties for the related copulas. Computational issues, approximations and random variate generation problems are addressed and simple numerical experiments to test the approximations developed are also performed. In particular, we propose an approximation to the copulas derived which we show to converge uniformly to the true copula. To illustrate the usefulness of the theory, we derive a fast procedure to estimate the underlying parameter in Manneville-Pomeau processes