Moderate deviations for the total population arising from a nearly unstable sub-critical Galton-Watson process with immigration

2019 ◽  
pp. 1-14
Author(s):  
Haotian Chen ◽  
Yong Zhang
Keyword(s):  
Total Population ◽  
Moderate Deviations ◽  
Watson Process

Estimation of the parameters of a branching process from migrating binomial observations

1998 ◽  
Vol 30 (4) ◽  
pp. 948-967 ◽  
Author(s):  
C. Jacob ◽  
J. Peccoud
Keyword(s):  
Confidence Interval ◽  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Total Population ◽  
Initial Population ◽  
Asymptotic Confidence Interval ◽  
Total Population Size ◽  
Initial Population Size ◽  
Watson Process

This paper considers a branching process generated by an offspring distribution F with mean m < ∞ and variance σ2 < ∞ and such that, at each generation n, there is an observed δ-migration, according to a binomial law Bpvn*Nnbef which depends on the total population size Nnbef. The δ-migration is defined as an emigration, an immigration or a null migration, depending on the value of δ, which is assumed constant throughout the different generations. The process with δ-migration is a generation-dependent Galton-Watson process, whereas the observed process is not in general a martingale. Under the assumption that the process with δ-migration is supercritical, we generalize for the observed migrating process the results relative to the Galton-Watson supercritical case that concern the asymptotic behaviour of the process and the estimation of m and σ2, as n → ∞. Moreover, an asymptotic confidence interval of the initial population size is given.

scholarly journals Wright–Fisher-like models with constant population size on average

2017 ◽  
Vol 10 (06) ◽  
pp. 1750078 ◽  
Author(s):  
Nicolas Grosjean ◽  
Thierry Huillet
Keyword(s):  
Population Genetics ◽  
Population Size ◽  
Discrete Time ◽  
Total Population ◽  
Neutral Evolution ◽  
Bottleneck Effect ◽  
Total Population Size ◽  
Constant Size ◽  
Basic Facts ◽  
Watson Process

We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton–Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment.

Estimation of the parameters of a branching process from migrating binomial observations

1998 ◽  
Vol 30 (04) ◽  
pp. 948-967 ◽  
Author(s):  
C. Jacob ◽  
J. Peccoud
Keyword(s):  
Confidence Interval ◽  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Total Population ◽  
Initial Population ◽  
Asymptotic Confidence Interval ◽  
Total Population Size ◽  
Initial Population Size ◽  
Watson Process

This paper considers a branching process generated by an offspring distribution F with mean m &lt; ∞ and variance σ2 &lt; ∞ and such that, at each generation n, there is an observed δ-migration, according to a binomial law B p v n *N n bef which depends on the total population size N n bef. The δ-migration is defined as an emigration, an immigration or a null migration, depending on the value of δ, which is assumed constant throughout the different generations. The process with δ-migration is a generation-dependent Galton-Watson process, whereas the observed process is not in general a martingale. Under the assumption that the process with δ-migration is supercritical, we generalize for the observed migrating process the results relative to the Galton-Watson supercritical case that concern the asymptotic behaviour of the process and the estimation of m and σ2, as n → ∞. Moreover, an asymptotic confidence interval of the initial population size is given.

From the Oort cloud to Halley-type comets

1999 ◽  
Vol 173 ◽  
pp. 327-338 ◽  
Author(s):  
J.A. Fernández ◽  
T. Gallardo
Keyword(s):  
Total Population ◽  
Complex Function ◽  
Dynamical Evolution ◽  
Oort Cloud ◽  
Capture Process ◽  
Influx Rate ◽  
Short Period ◽  
Dynamical Properties ◽  
Orbital Periods ◽  
Probability Of Capture

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods &lt; 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq &lt;2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods &lt; 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.

Concerning the Representativeness of Psychiatric Catamnestical Studies - The Influence of Various Approach Strategies on the Response of Former Patients

1986 ◽  
Vol 25 (03) ◽  
pp. 171-175
Author(s):  
I. Steinhart ◽  
G. Bosch ◽  
Th. Muhr ◽  
E. Mohlfeld
Keyword(s):  
Total Population ◽  
Social Psychiatry ◽  
Personal Contact ◽  
Sample Collection ◽  
Careful Planning ◽  
Research Project ◽  
Phone Calls ◽  
Registration Procedure

SummaryThe possible conclusions reached by catamnestical studies are often significantly restricted because of the lack of representativeness of the sample. The example of an investigation of former patients of the Department of Social Psychiatry proves that positive responses to an interview are influenced by various factors. As expected, patients were more inclined to participate in the research project the closer their discharge was to the time of the project itself. Further, it became clear that various different approach strategies, such as letters, enquiries with the registration authorities, phone calls and house visits, effectively increased the motivation of former patients, and that only this kind of graded registration procedure guarantees motivation leading to a sample representative of the total population. Personal contact plays an especially important role. These empirical findings indicate the necessity of careful planning and implementation of sample collection in catamnestical studies. Without this approach, representative results cannot be expected.

Management of Haemophilia in Sweden

1976 ◽  
Vol 35 (03) ◽  
pp. 510-521 ◽  
Author(s):  
Inga Marie Nilsson
Keyword(s):  
Factor Viii ◽  
Total Population ◽  
Age Groups ◽  
Factor Ix ◽  
Haemophilia A ◽  
Severe Haemophilia ◽  
Haemophilia B ◽  
Human Fraction ◽  
Mild Haemophilia

SummaryThe incidence of living haemophiliacs in Sweden (total population 8.1 millions) is about 1:15,000 males and about 1:30,000 of the entire population. The number of haemophiliacs born in Sweden in 5-year periods between 1931-1975 (June) has remained almost unchanged. The total number of haemophilia families in Sweden is 284 (77% haemophilia A, 23% haemophilia B) with altogether 557 (436 with A and 121 with B) living haemophiliacs. Of the haemophilia A patients 40 % have severe, 18 % moderate, and 42 % mild, haemophilia. The distribution of the haemophilia B patients is about the same. Inhibitors have been demonstrated in 8% of the patients with severe haemophilia A and in 10% of those with severe haemophilia B.There are 2 main Haemophilia Centres (Stockholm, Malmo) to which haemophiliacs from the whole of Sweden are admitted for diagnosis, follow-up and treatment for severe bleedings, joint defects and surgery. Minor bleedings are treated at local hospitals in cooperation with the Haemophilia Centres. The concentrates available for treatment in haemophilia A are human fraction 1-0 (AHF-Kabi), cryoprecipitate, Antihaemophilic Factor (Hyland 4) and Kryobulin (Immuno, Wien). AHF-Kabi is the most commonly used preparation. The concentrates available for treatment in haemophilia B are Preconativ (Kabi) and Prothromplex (Immuno). Sufficient amounts of concentrates are available. In Sweden 3.2 million units of factor VIII and 1.0 million units of factor IX are given per year. Treatment is free of charge.Only 5 patients receive domiciliary treatment, but since 1958 we in Sweden have practised prophylactic treatment of boys (4–18 years old) with severe haemophilia A. At about 5-10 days interval they receive AHF in amounts sufficient to raise the AHF level to 40–50%. This regimen has reduced severe haemophilia to moderate. The joint score is identical with that found in moderate haemophilia in the same age groups. For treatment of patients with haemophilia A and haemophilia B complicated by inhibitors we have used a large dose of antigen (factor VIII or factor IX) combined with cyclophosphamide. In most cases this treatment produced satisfactory haemostasis for 5 to 30 days and prevented the secondary antibody rise.

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