A note on a universal random variate generator for integer-valued random variables

@article{Barabesi2014ANO,
  title={A note on a universal random variate generator for integer-valued random variables},
  author={Lucio Barabesi and Luca Pratelli},
  journal={Statistics and Computing},
  year={2014},
  volume={24},
  pages={589-596}
}
A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. This approach allows to create a dominating probability function, whose evaluation solely involves two integrals depending on the characteristic function of the random variable to be generated. The proposal gives rise to a simple algorithm which may be implemented in a few… 
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References

SHOWING 1-10 OF 30 REFERENCES
Automatic Nonuniform Random Variate Generation
TLDR
It is shown how random variate genration algorithms work and an interface for R is suggested as an example of a statistical library, which could be used for simulation or statistical computing.
A simple universal generator for continuous and discrete univariate T-concave distributions
We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave…
Random variate generation for exponentially and polynomially tilted stable distributions
TLDR
This work develops exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions and presents a novel double rejection method that is useful whenever densities have an integral representation involving an auxiliary variable.
On the computer generation of random variables with a given characteristic function
Non-Uniform Random Variate Generation
TLDR
This chapter reviews the main methods for generating random variables, vectors and processes in non-uniform random variate generation, and provides information on the expected time complexity of various algorithms before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.
Generating random numbers from a distribution specified by its Laplace transform
TLDR
This paper advocates simulation by the inversion method using a modified Newton-Raphson method, with values of the distribution and density functions obtained by numerical transform inversion, and shows that this algorithm performs well in a series of increasingly complex examples.
Algorithms for Generating Discrete Random Variables with a Given Generating Function or a Given Moment Sequence
The author presents and analyzes various algorithms for generating positive integer-valued random variables when the distribution is described either through the generating function $\sum _{i =…
Short universal generators via generalized ratio-of-uniforms method
  • J. Leydold
  • Mathematics, Computer Science
    Math. Comput.
  • 2003
We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave…
A simple generator for discrete log-concave distributions
  • L. Devroye
  • Mathematics, Computer Science
    Computing
  • 2006
We give a short algorithm that can be used to generate random integers with a log-concave distribution (such as the binomial, Poisson, hypergeometric, negative binomial, geometric, logarithmic series…
Parameter Estimation for the Discrete Stable Family
The discrete stable family constitutes an interesting two-parameter model of distributions on the non-negative integers with a Paretian tail. The practical use of the discrete stable distribution is…
...
...