Exact simulation of two-parameter Poisson-Dirichlet random variables

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

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Density approximation and exact simulation of random variables that are solutions of fixed-point equations

Advances in Applied Probability ◽

10.1017/s0001867800011642 ◽

2002 ◽

Vol 34 (02) ◽

pp. 441-468 ◽

Cited By ~ 2

Author(s):

Luc Devroye ◽

Ralph Neininger

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Error Bounds ◽

Probabilistic Analysis ◽

Analysis Of Algorithms ◽

Random Variables ◽

Probability Measures ◽

Density Approximation ◽

Exact Simulation ◽

Probabilistic Analysis Of Algorithms

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

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Exact simulation of generalised Vervaat perpetuities

Journal of Applied Probability ◽

10.1017/jpr.2019.6 ◽

2019 ◽

Vol 56 (01) ◽

pp. 57-75 ◽

Cited By ~ 3

Author(s):

Angelos Dassios ◽

Yan Qu ◽

Jia Wei Lim

Keyword(s):

Numerical Analysis ◽

General Framework ◽

Random Variables ◽

Gamma Process ◽

Simulation Algorithm ◽

Decomposition Technique ◽

Exact Simulation ◽

Case Examples ◽

Novel Method ◽

Special Case

AbstractWe consider a generalised Vervaat perpetuity of the form X = Y1W1 +Y2W1W2 + · · ·, where $W_i \sim {\cal U}^{1/t}$ and (Yi)i≥0 is an independent and identically distributed sequence of random variables independent from (Wi)i≥0. Based on a distributional decomposition technique, we propose a novel method for exactly simulating the generalised Vervaat perpetuity. The general framework relies on the exact simulation of the truncated gamma process, which we develop using a marked renewal representation for its paths. Furthermore, a special case arises when Yi = 1, and X has the generalised Dickman distribution, for which we present an exact simulation algorithm using the marked renewal approach. In particular, this new algorithm is much faster than existing algorithms illustrated in Chi (2012), Cloud and Huber (2017), Devroye and Fawzi (2010), and Fill and Huber (2010), as well as being applicable to the general payments case. Examples and numerical analysis are provided to demonstrate the accuracy and effectiveness of our method.

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An Arc-Sine Law for Last Hitting Points in the Two-Parameter Wiener Space

Mathematics ◽

10.3390/math7111131 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1131

Author(s):

Jeong-Gyoo KIM

Keyword(s):

Stochastic Process ◽

Wiener Process ◽

Random Variables ◽

Hitting Time ◽

Wiener Space ◽

Key Factor ◽

Two Parameters ◽

Sine Law ◽

Two Parameter

We develop the two-parameter version of an arc-sine law for a last hitting time. The existing arc-sine laws are about a stochastic process X t with one parameter t. If there is another varying key factor of an event described by a process, then we need to consider another parameter besides t. That is, we need a system of random variables with two parameters, say X s , t , which is far more complex than one-parameter processes. In this paper we challenge to develop such an idea, and provide the two-parameter version of an arc-sine law for a last hitting time. An arc-sine law for a two-parameter process is hardly found in literature. We use the properties of the two-parameter Wiener process for our development. Our result shows that the probability of last hitting points in the two-parameter Wiener space turns out to be arcsine-distributed. One can use our results to predict an event happened in a system of random variables with two parameters, which is not available among existing arc-sine laws for one parameter processes.

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Normal approximations to discrete unimodal distributions

Journal of Applied Probability ◽

10.1017/s0021900200115931 ◽

1986 ◽

Vol 23 (04) ◽

pp. 1013-1018

Author(s):

B. G. Quinn ◽

H. L. MacGillivray

Keyword(s):

Stationary Distribution ◽

Sufficient Conditions ◽

Random Variables ◽

Hypergeometric Distribution ◽

Death Process ◽

Normal Approximations ◽

Discrete Random Variables ◽

Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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Some results of the Barbier-Chalonge-Divan system of stellar classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053250 ◽

1966 ◽

Vol 24 ◽

pp. 77-90 ◽

Cited By ~ 1

Author(s):

D. Chalonge

Keyword(s):

Early Type ◽

Parameter System ◽

Early Type Stars ◽

Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

Zeitschrift für Sozialpsychologie ◽

10.1024//0044-3514.32.3.133 ◽

2001 ◽

Vol 32 (3) ◽

pp. 133-141 ◽

Cited By ~ 4

Author(s):

Gerrit Antonides ◽

Sophia R. Wunderink

Keyword(s):

Willingness To Pay ◽

Energy Saving ◽

Subjective Time ◽

Durable Good ◽

Discount Function ◽

Hyperbolic Discount ◽

The One ◽

Two Parameter ◽

Difference Effect ◽

Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

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