Efficient Simulation of the von Mises Distribution

Best, D. J.; Fisher, N. I.

doi:10.2307/2346732

Cited by 167 publications

(131 citation statements)

References 8 publications

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“…A total of 10,000 sets of N samples are generated using the vMUM statistical model. The random samples are generated using the algorithm proposed by Best and Fisher [15]. For each set, the parameters are drawn from uniform distributions with μ ∼ U(0, 2π), κ ∼ U(0, 100), p 2 ∼ U(0, 0.3) and p 3 ∼ U(0, 0.3), where the symbol ∼ stands for "distributed as."…”

Section: Performance Analysis Of Parameter Estimationmentioning

confidence: 99%

Localization Experiments with Reporting by Head Orientation: Statistical Framework and Case Study

Sena¹,

Brookes²,

Naylor³

et al. 2017

J. Audio Eng. Soc.

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This paper is concerned with sound localization experiments in which subjects report the position of an active sound source by turning toward it. A statistical framework for the analysis of the data from this type of experiment is presented together with a case study from a largescale listening experiment. The statistical framework is based on a model that is robust to the presence of front/back confusions and random errors. Closed-form natural estimators are derived, and one-sample and two-sample statistical tests are presented. The framework is used to analyze the data of an auralized experiment undertaken by nearly nine hundred subjects. Results show that responses had a rightward bias and that speech was harder to localize than percussion sounds, which are results consistent with the literature. Results also show that it was harder to localize sound in a simulated room with high ceiling, despite having a higher direct-to-reverberant ratio than other simulated rooms.

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Section: Performance Analysis Of Parameter Estimationmentioning

confidence: 99%

Localization Experiments with Reporting by Head Orientation: Statistical Framework and Case Study

Sena¹,

Brookes²,

Naylor³

et al. 2017

J. Audio Eng. Soc.

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“…After determining the direction of bias from Equation 4, we must choose in which direction the agent will move. The direction, θ, is drawn from a von Mises distribution (also known as the Circular Normal distribution) [33,26,5]. For θ ∈ [−π, π], the von Mises distribution is given by…”

Section: Process Overview and Schedulingmentioning

confidence: 99%

Geographical influences of an emerging network of gang rivalries

Hegemann¹,

Smith²,

Barbaro³

et al. 2011

Physica A: Statistical Mechanics and its Applications

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We propose an agent-based model to simulate the creation of street gang rivalries. The movement dynamics of agents are coupled to an evolving network of gang rivalries, which is determined by previous interactions among agents in the system. Basic gang data, geographic information, and behavioral dynamics suggested by the criminology literature are integrated into the model. The major highways, rivers, and the locations of gangs' centers of activity influence the agents' motion. We use a policing division of the Los Angeles Police Department as a case study to test our model. We use common metrics from graph theory to analyze our model, comparing networks produced by our simulations and an instance of a Geographical Threshold Graph to the network existing in the criminology literature.

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“…For example, employing the method of Best and Fisher (1979), which is an acceptance/rejection algorithm based, intrigu-ingly, on an envelope proportional to the wrapped Cauchy density, a random number from model (2) is generated by the following algorithm. First, set…”

Section: Random Variate Generationmentioning

confidence: 99%

A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation

Kato

Jones

2010

Journal of the American Statistical Association

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We propose a family of four-parameter distributions on the circle that contains the von Mises and wrapped Cauchy distributions as special cases. The family is derived by transforming the von Mises distribution via Möbius transformation which maps the unit circle onto itself.The densities in the family have a symmetric or asymmetric, unimodal or bimodal shape, depending on the values of parameters. Conditions for unimodality are explored. Further properties of the proposed model are obtained, many by applying the theory of the Möbius transformation. Properties of a three-parameter symmetric submodel are also investigated; these include maximum likelihood estimation, its asymptotics and a reparametrisation that proves useful quite generally. A three-parameter asymmetric subfamily, which proves adequate in each of the examples in the paper, is also discussed with emphasis on its mean direction and circular skewness. The proposed family and subfamilies are used to model an asymmetrically distributed dataset and are then adopted as the angular error distribution of a circular-circular regression model, and an application given thereof. It is in this regression context that the Möbius transformation particularly comes into its own. Comparisons with other families of circular distributions are made.

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Efficient Simulation of the von Mises Distribution

Abstract: Summary An algorithm is given to simulate samples from the von Mises distribution. A wrapped Cauchy density is used as an envelope to give an acceptance–rejection method which is both simple to program and fast for all values of the concentration parameter of the von Mises distribution.

Cited by 167 publications

References 8 publications

Localization Experiments with Reporting by Head Orientation: Statistical Framework and Case Study

Localization Experiments with Reporting by Head Orientation: Statistical Framework and Case Study

Geographical influences of an emerging network of gang rivalries

A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation

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