Asymptotic behaviour of immigration-branching processes with general set of types. I: Critical branching part

1973 ◽  
Vol 5 (3) ◽  
pp. 391-416 ◽  
Author(s):  
H. Hering
Keyword(s):  
Probability Distributions ◽  
Branching Processes ◽  
Weak Form ◽  
Transition Function ◽  
Functional Method ◽  
Distribution Functions ◽  
Generating Functional ◽  
Second Moments ◽  
Vector Valued ◽  
Population Probability

We consider immigration-branching processes constructable from an inhomogeneous Poisson process, a sequence of population probability distributions, and a homogeneous branching transition function. The set of types is arbitrary, and the process parameter is allowed to be discrete or continuous. For the branching part a weak form of positive regularity, criticality, and the existence of second moments are assumed. Varying the conditions on the immigration law, we obtain several results concerning asymptotic extinction, the rate of extinction, and limiting distribution functions of properly normalized, vector-valued counting processes associated with the immigration branching process. The proofs are based on the generating functional method.

Asymptotic behaviour of immigration-branching processes with general set of types. I: Critical branching part

1973 ◽  
Vol 5 (03) ◽  
pp. 391-416 ◽  
Author(s):  
H. Hering
Keyword(s):  
Probability Distributions ◽  
Branching Processes ◽  
Weak Form ◽  
Transition Function ◽  
Functional Method ◽  
Distribution Functions ◽  
Generating Functional ◽  
Second Moments ◽  
Vector Valued ◽  
Population Probability

We consider immigration-branching processes constructable from an inhomogeneous Poisson process, a sequence of population probability distributions, and a homogeneous branching transition function. The set of types is arbitrary, and the process parameter is allowed to be discrete or continuous. For the branching part a weak form of positive regularity, criticality, and the existence of second moments are assumed. Varying the conditions on the immigration law, we obtain several results concerning asymptotic extinction, the rate of extinction, and limiting distribution functions of properly normalized, vector-valued counting processes associated with the immigration branching process. The proofs are based on the generating functional method.

Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

1975 ◽  
Vol 7 (03) ◽  
pp. 468-494
Author(s):  
H. Hering
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Transition Function ◽  
Mean Square ◽  
Second Moments ◽  
Mean Square Convergence ◽  
The Mean ◽  
Parameter Dependent ◽  
Dependent Probability

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

1975 ◽  
Vol 7 (3) ◽  
pp. 468-494
Author(s):  
H. Hering
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Transition Function ◽  
Mean Square ◽  
Second Moments ◽  
Mean Square Convergence ◽  
The Mean ◽  
Parameter Dependent ◽  
Dependent Probability

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

scholarly journals Verb valency in interlanguage: An extension to valency theory and new perspective on L2 learning

2020 ◽  
Vol 56 (2) ◽  
pp. 339-363
Author(s):  
Qianying Zhao ◽  
Jingyang Jiang
Keyword(s):  
Probability Distributions ◽  
Specific Property ◽  
Distribution Functions ◽  
Target Language ◽  
Native Languages ◽  
Language Competence ◽  
English Writing ◽  
Chinese Learners ◽  
L2 Learning ◽  
New Perspective

AbstractValency theory has been applied to investigate various languages, such as German, Chinese and English. However, most studies in this field were based on the linguistic materials produced by native speakers. The current research aimed to examine the valency structures in the interlanguage. Based on the English writing produced by L2 Chinese learners, we adopted the quantitative approach, trying to find out whether the distributional features of verb valency in the interlanguage also had regular probability distributions as those in the native languages, and whether there was a relationship between these valency distributional characteristics and L2 learners’ language competence. It was found that (1) verb valency in the interlanguage followed distributional regularities which had been identified in the native languages; (2) the valency features showed differences in the diversity of valency patterns, the use of valences and the complexity of forms of complements between the interlanguage and the target language; (3) the distribution functions and parameters related to verb valency could manifest the development of students’ language competence. The current research has extended valency theory to the study of interlanguage and the valency perspective has profound methodological and pedagogical implications for L2 learning. Its item-specific property and the integration of grammatical and lexical factors are conducive to analyzing the way various words combine with each other.

On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (04) ◽  
pp. 965-981 ◽  
Author(s):  
S. G. Foss ◽  
S. A. Zuyev
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Distribution Functions ◽  
Poisson Processes ◽  
Upper And Lower Bounds ◽  
Additive Functionals ◽  
Second Moments ◽  
Explicit Formulae ◽  
Bivariate Poisson Process ◽  
Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

scholarly journals Probabilistic Precipitation Forecast Postprocessing Using Quantile Mapping and Rank-Weighted Best-Member Dressing

2018 ◽  
Vol 146 (12) ◽  
pp. 4079-4098 ◽  
Author(s):  
Thomas M. Hamill ◽  
Michael Scheuerer
Keyword(s):  
Probability Distributions ◽  
The United States ◽  
Ensemble Forecast ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Precipitation Forecast ◽  
Prediction System ◽  
Quantile Mapping ◽  
State Dependent ◽  
Grid Points

Abstract Hamill et al. described a multimodel ensemble precipitation postprocessing algorithm that is used operationally by the U.S. National Weather Service (NWS). This article describes further changes that produce improved, reliable, and skillful probabilistic quantitative precipitation forecasts (PQPFs) for single or multimodel prediction systems. For multimodel systems, final probabilities are produced through the linear combination of PQPFs from the constituent models. The new methodology is applied to each prediction system. Prior to adjustment of the forecasts, parametric cumulative distribution functions (CDFs) of model and analyzed climatologies are generated using the previous 60 days’ forecasts and analyses and supplemental locations. The CDFs, which can be stored with minimal disk space, are then used for quantile mapping to correct state-dependent bias for each member. In this stage, the ensemble is also enlarged using a stencil of forecast values from the 5 × 5 surrounding grid points. Different weights and dressing distributions are assigned to the sorted, quantile-mapped members, with generally larger weights for outlying members and broader dressing distributions for members with heavier precipitation. Probability distributions are generated from the weighted sum of the dressing distributions. The NWS Global Ensemble Forecast System (GEFS), the Canadian Meteorological Centre (CMC) global ensemble, and the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecast data are postprocessed for April–June 2016. Single prediction system postprocessed forecasts are generally reliable and skillful. Multimodel PQPFs are roughly as skillful as the ECMWF system alone. Postprocessed guidance was generally more skillful than guidance using the Gamma distribution approach of Scheuerer and Hamill, with coefficients generated from data pooled across the United States.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Notes on statistical ensembles in the Cell Model

2020 ◽  
Vol 29 (08) ◽  
pp. 2050060
Author(s):  
M. Gazdzicki ◽  
M. I. Gorenstein ◽  
O. Savchuk ◽  
L. Tinti
Keyword(s):  
Statistical Physics ◽  
Cell Model ◽  
Probability Distributions ◽  
Joint Probability ◽  
Second Moments ◽  
Statistical Ensembles ◽  
Volume Limit ◽  
Joint Probability Distributions ◽  
Infinite Volume Limit ◽  
Number Of Particles

Properties of basic statistical ensembles in the Cell Model are discussed. The simplest version of the model with a fixed total number of particles is considered. The microcanonical ensembles of distinguishable and indistinguishable particles, with and without a limit on the maximum number of particles in a single cell, are discussed. The joint probability distributions of particle multiplicities in cells for different ensembles are derived, and their second moments are calculated. The results for infinite volume limit are calculated. The obtained results resemble those in the statistical physics of bosons, fermions and boltzmanions.

Generating functional method for spin variables

1973 ◽  
Vol 16 (2) ◽  
pp. 820-829 ◽  
Author(s):  
S. V. Peletminskii ◽  
A. A. Yatsenko
Keyword(s):  
Functional Method ◽  
Generating Functional
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