scholarly journals Computational Simulations of Similar Probabilistic Distributions to the Binomial and Poisson Distributions

2020 ◽  
Author(s):  
Terman Frometa-Castillo ◽  
Anil Pyakuryal ◽  
Amadeo Wals-Zurita ◽  
Asghar Mesbahi
Keyword(s):  
Poisson Distribution ◽  
Statistical Models ◽  
Success Probability ◽  
Discrete Variable ◽  
Computational Simulations ◽  
Maximum Probability ◽  
Upper Limit ◽  
Probabilistic Distribution ◽  
Poisson Distributions ◽  
Poisson Parameter

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these legendary distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of the random discrete variable X. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

scholarly journals Computational Simulations of Similar Probabilistic Distributions to the Binomial and Poisson Distributions

2020 ◽  
Author(s):  
Terman Frometa-Castillo ◽  
Anil Pyakuryal ◽  
Amadeo Wals-Zurita ◽  
Asghar Mesbahi
Keyword(s):  
Poisson Distribution ◽  
Statistical Models ◽  
Success Probability ◽  
Discrete Variable ◽  
Computational Simulations ◽  
Maximum Probability ◽  
Upper Limit ◽  
Probabilistic Distribution ◽  
Poisson Distributions ◽  
Poisson Parameter

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these popular distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is the upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of a random discrete variable. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

On a characterization of Poisson distributions

1972 ◽  
Vol 9 (4) ◽  
pp. 852-856 ◽  
Author(s):  
J. Aczél
Keyword(s):  
Poisson Distribution ◽  
Random Variables ◽  
Mutual Dependence ◽  
Binomial Distributions ◽  
Destructive Process ◽  
Poisson Distributions ◽  
Bivariate Poisson Distribution

The conjecture pronounced at the end of the paper of Srivastava and Srivastava (1970) is proved in this paper. It gives the following characterization of (bivariate) Poisson distributions. Suppose that items of two types have been observed certain numbers of times, but these original observations have been reduced due to a destructive process which is the product of two binomial distributions and that the probabilities of these reduced numbers are the same whether damaged or undamaged. Then the original random variables had a bivariate Poisson distribution with zero mutual dependence coefficient.

Warm Season Lightning Probability Prediction for Canada and the Northern United States

2005 ◽  
Vol 20 (6) ◽  
pp. 971-988 ◽  
Author(s):  
William R. Burrows ◽  
Colin Price ◽  
Laurence J. Wilson
Keyword(s):  
Statistical Models ◽  
Prediction Models ◽  
Grid Point ◽  
Warm Season ◽  
Precipitable Water ◽  
Large Area ◽  
Maximum Probability ◽  
The North ◽  
The Mean ◽  
Structured Regression

Abstract Statistical models valid May–September were developed to predict the probability of lightning in 3-h intervals using observations from the North American Lightning Detection Network and predictors derived from Global Environmental Multiscale (GEM) model output at the Canadian Meteorological Centre. Models were built with pooled data from the years 2000–01 using tree-structured regression. Error reduction by most models was about 0.4–0.7 of initial predictand variance. Many predictors were required to model lightning occurrence for this large area. Highest ranked overall were the Showalter index, mean sea level pressure, and troposphere precipitable water. Three-hour changes of 500-hPa geopotential height, 500–1000-hPa thickness, and MSL pressure were highly ranked in most areas. The 3-h average of most predictors was more important than the mean or maximum (minimum where appropriate). Several predictors outranked CAPE, indicating it must appear with other predictors for successful statistical lightning prediction models. Results presented herein demonstrate that tree-structured regression is a viable method for building statistical models to forecast lightning probability. Real-time forecasts in 3-h intervals to 45–48 h were made in 2003 and 2004. The 2003 verification suggests a hybrid forecast based on a mixture of maximum and mean forecast probabilities in a radius around a grid point and on monthly climatology will improve accuracy. The 2004 verification shows that the hybrid forecasts had positive skill with respect to a reference forecast and performed better than forecasts defined by either the mean or maximum probability at most times. This was achieved even though an increase of resolution and change of convective parameterization scheme were made to the GEM model in May 2004.

scholarly journals On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 845
Author(s):  
Sergei Nagaev ◽  
Vladimir Chebotarev
Keyword(s):  
Poisson Distribution ◽  
Error Estimates ◽  
Correction Factor ◽  
Mathematical Expectation ◽  
Binomial Distribution ◽  
Poisson Approximation ◽  
Kolmogorov Distance ◽  
Poisson Law ◽  
Poisson Distributions ◽  
New Type

A subject of this study is the behavior of the tail of the binomial distribution in the case of the Poisson approximation. The deviation from unit of the ratio of the tail of the binomial distribution and that of the Poisson distribution, multiplied by the correction factor, is estimated. A new type of approximation is introduced when the parameter of the approximating Poisson law depends on the point at which the approximation is performed. Then the transition to the approximation by the Poisson law with the parameter equal to the mathematical expectation of the approximated binomial law is carried out. In both cases error estimates are obtained. A number of conjectures are made about the refinement of the known estimates for the Kolmogorov distance between binomial and Poisson distributions.

scholarly journals Actuarial Evaluation of Late Losses: A Chain Ladder Model or a Generalized Linear Model of Rated Loss Increaments with a Poisson Distribution?

2020 ◽  
pp. 87-91
Author(s):  
Aleksey Vladimirovich Tanyukhin
Keyword(s):  
Linear Model ◽  
Poisson Distribution ◽  
Generalized Linear Model ◽  
Incremental Development ◽  
Ladder Model ◽  
Poisson Distributions ◽  
Chain Ladder ◽  
A Chain ◽  
Development Triangle

This article focuses on the equality of the estimated late losses resulting from the application of the chain ladder model to the estimates obtained on the basis of the incremental development triangle by cross-parameterizing the rated increments of losses with Poisson distributions using the generalized linear model. In this article, the formulas of the chain ladder model are derived by solving the problem of cross parameterization of rated increments of losses. Smaller accounting groups than the risk, along which the development triangle is formed, make conclusions about the possible bases for the sharing of reserves. This issue may be relevant for the further calculation of actuarial premiums.

scholarly journals Coverage Strategy for Target Location in Marine Environments Using Fixed-Wing UAVs

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 120
Author(s):  
Javier Muñoz ◽  
Blanca López ◽  
Fernando Quevedo ◽  
Concepción A. Monje ◽  
Santiago Garrido ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Target Location ◽  
Differential Evolution Algorithm ◽  
Maximum Probability ◽  
Sweep Angle ◽  
Data Set ◽  
Probabilistic Distribution ◽  
Sweep Direction ◽  
Gaussian Probability Distribution ◽  
Evolution Algorithm

In this paper, we propose a coverage method for the search of lost target or debris on the ocean surface. The OSCAR data set is used to determine the marine currents and the differential evolution genetic filter is used to optimize the sweep direction of the lawnmower coverage and get the sweep angle for the maximum probability of containment. The position of the target is determined by a particle filter, where the particles are moved by the ocean currents and the final probabilistic distribution is obtained by fitting the particle positions to a Gaussian probability distribution. The differential evolution algorithm is then used to optimize the sweep direction that covers the highest probability of containment cells before the less probable ones. The algorithm is tested with a variety of parameters of the differential evolution algorithm and compared to other popular optimization algorithms.

On a characterization of Poisson distributions

1972 ◽  
Vol 9 (04) ◽  
pp. 852-856 ◽  
Author(s):  
J. Aczél
Keyword(s):  
Poisson Distribution ◽  
Random Variables ◽  
Mutual Dependence ◽  
Binomial Distributions ◽  
Destructive Process ◽  
Poisson Distributions ◽  
Bivariate Poisson Distribution

The conjecture pronounced at the end of the paper of Srivastava and Srivastava (1970) is proved in this paper. It gives the following characterization of (bivariate) Poisson distributions. Suppose that items of two types have been observed certain numbers of times, but these original observations have been reduced due to a destructive process which is the product of two binomial distributions and that the probabilities of these reduced numbers are the same whether damaged or undamaged. Then the original random variables had a bivariate Poisson distribution with zero mutual dependence coefficient.

scholarly journals The Mixed Bivariate Hofmann Distribution

2001 ◽  
Vol 31 (1) ◽  
pp. 123-138 ◽  
Author(s):  
J.F. Walhin ◽  
J. Paris
Keyword(s):  
Poisson Distribution ◽  
Gaussian Distribution ◽  
Negative Binomial ◽  
Inverse Gaussian Distribution ◽  
Inverse Gaussian ◽  
Bivariate Case ◽  
Univariate Case ◽  
Poisson Distributions ◽  
Aggregate Claims

AbstractIn this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case.We show how to evaluate the bivariate aggregate claims distribution and we fit some insurance portfolios given in the literature.This study typically extends the use of the Bivariate Independent Poisson Distribution, the Mixed Bivariate Negative Binomial and the Mixed Bivariate Poisson Inverse Gaussian Distribution.

scholarly journals Compound bi-free Poisson distributions

2019 ◽  
Vol 22 (02) ◽  
pp. 1950014
Author(s):  
Mingchu Gao
Keyword(s):  
Poisson Distribution ◽  
Matrix Model ◽  
Random Variables ◽  
Divisible Distribution ◽  
Infinitely Divisible Distribution ◽  
Infinitely Divisible ◽  
Random Matrix Model ◽  
Poisson Distributions ◽  
Poisson Limit ◽  
The Right

In this paper, we study compound bi-free Poisson distributions for two-faced families of random variables. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible distribution for a two-faced family of self-adjoint random variables can be realized as the limit of a sequence of compound bi-free Poisson distributions of two-faced families of self-adjoint random variables. If a compound bi-free Poisson distribution is determined by a positive number and the distribution of a two-faced family of finitely many random variables, which has an almost sure random matrix model, and the left random variables commute with the right random variables in the two-faced family, then we can construct a random bi-matrix model for the compound bi-free Poisson distribution. If a compound bi-free Poisson distribution is determined by a positive number and the distribution of a commutative pair of random variables, we can construct an asymptotic bi-matrix model with entries of creation and annihilation operators for the compound bi-free Poisson distribution.

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