Poisson-saddlepoint approximation for Gibbs point processes with infinite-order interaction: in memory of Peter Hall

2017 ◽  
Vol 54 (4) ◽  
pp. 1008-1026
Author(s):  
Adrian Baddeley ◽  
Gopalan Nair
Keyword(s):  
Point Processes ◽  
Infinite Order ◽  
Saddlepoint Approximation ◽  
Moment Generating Function ◽  
Small Sample ◽  
Sufficient Statistic ◽  
Scaling Properties ◽  
Gibbs Point Processes ◽  
The Moment ◽  
Self Consistency

Abstract We develop a computational approximation to the intensity of a Gibbs spatial point process having interactions of any order. Limit theorems from stochastic geometry, and small-sample probabilities estimated once and for all by an extensive simulation study, are combined with scaling properties to form an approximation to the moment generating function of the sufficient statistic under a Poisson process. The approximate intensity is obtained as the solution of a self-consistency equation.

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

scholarly journals Fast approximation of the intensity of Gibbs point processes

2012 ◽  
Vol 6 (0) ◽  
pp. 1155-1169 ◽  
Author(s):  
Adrian Baddeley ◽  
Gopalan Nair
Keyword(s):  
Point Processes ◽  
Gibbs Point Processes

scholarly journals The ruin problem for a Wiener process with state-dependent jumps

2020 ◽  
Vol 16 (1) ◽  
pp. 13-23
Author(s):  
M. Lefebvre
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Jump Diffusion ◽  
Moment Generating Function ◽  
Continuous Part ◽  
State Dependent ◽  
The Moment ◽  
First Time

AbstractLet X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

scholarly journals Tornumonkpe Distribution: Statistical Properties and Goodness of Fit

2021 ◽  
pp. 12-22
Author(s):  
Barinaadaa John Nwikpe
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Mathematical Expression ◽  
Information Criterion ◽  
Moment Generating Function ◽  
Data Sets ◽  
The Moment ◽  
The One ◽  
Coefficient Of Skewness ◽  
New Distribution

A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2,  and gamma(3  distributions. The shape of its density for different values of the parameter has been shown.  The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

scholarly journals Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1149 ◽  
Author(s):  
Hyojin Lee ◽  
Kyeongjun Lee
Keyword(s):  
Scale Parameter ◽  
Moment Generating Function ◽  
Likelihood Inference ◽  
Exponential Parameter ◽  
Hybrid Censoring ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
New Type ◽  
The Moment ◽  
Censoring Scheme

In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.

scholarly journals Exact Performance Analysis of Amplify-and-Forward Bidirectional Relaying over Nakagami-m Fading Channels with Arbitrary Parameters

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1277
Author(s):  
Dong Qin ◽  
Yuhao Wang ◽  
Tianqing Zhou
Keyword(s):  
Fading Channels ◽  
Signal To Noise Ratio ◽  
Ergodic Capacity ◽  
Moment Generating Function ◽  
Amplify And Forward ◽  
Relay Systems ◽  
Signal Error ◽  
Bidirectional Relaying ◽  
Fading Parameter ◽  
The Moment

The exact performance of amplify-and-forward (AF) bidirectional relay systems is studied in generalized and versatile Nakagami-m fading channels, where the parameter m is an arbitrary positive number. We consider three relaying modes: two, three, and four time slot bidirectional relaying. Closed form expressions of the moment generating function (MGF), higher order moments of signal-to-noise ratio (SNR), ergodic capacity, and average signal error probability (SEP) are derived, which are different from previous works. The obtained expressions are very concise, easy to calculate, and evaluated instantaneously without a complex summation operation, in contrast to the nested multifold numerical integrals and truncated infinite series expansions used in previous work, which lead to computational inefficiency, especially when the fading parameter m increases. Simulation results corroborate the correctness and tightness of the theoretical analysis.

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