On the exact transient solution of fluid queue driven by a birth death process with specific rational rates and absorption

OPSEARCH ◽  
2015 ◽  
Vol 52 (4) ◽  
pp. 746-755 ◽  
Author(s):  
Shruti Kapoor ◽  
Dharmaraja Selvamuthu
Keyword(s):  
Death Process ◽  
Transient Solution ◽  
Fluid Queue ◽  
Birth Death

scholarly journals Exact transient solution of a state-dependent birth-death process

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
P. R. Parthasarathy ◽  
R. Sudhesh
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Death Process ◽  
Transient Solution ◽  
State Dependent ◽  
Transient Probabilities ◽  
Series Expression ◽  
Birth Death

A power series expression in closed form for the transient probabilities of a state-dependent birth-death process is presented with suitable illustrations.

Transient solution of fluid queue modulated by two independent birth-death processes

2019 ◽  
Vol 36 (1) ◽  
pp. 1
Author(s):  
Viswanathan Arunachalam ◽  
Shruti Kapoor ◽  
Selvamuthu Dharmaraja
Keyword(s):  
Transient Solution ◽  
Fluid Queue ◽  
Birth Death

Transient solution of fluid queue modulated by two independent birth-death processes

2019 ◽  
Vol 36 (1) ◽  
pp. 1
Author(s):  
Shruti Kapoor ◽  
Selvamuthu Dharmaraja ◽  
Viswanathan Arunachalam
Keyword(s):  
Transient Solution ◽  
Fluid Queue ◽  
Birth Death

TRANSIENT SOLUTION FOR A SIMPLE IMMIGRATION BIRTH–DEATH CATASTROPHE PROCESS

2004 ◽  
Vol 18 (2) ◽  
pp. 233-236 ◽  
Author(s):  
E. G. Kyriakidis
Keyword(s):  
Death Process ◽  
Transient Solution ◽  
Transient Probabilities ◽  
Birth Death

In this note, we consider a simple immigration birth–death process with total catastrophes and we obtain the transient probabilities. Our approach involves a renewal argument. It is comparatively simpler and leads to more elegant expressions than other approaches that appeared in the literature recently.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

scholarly journals A generalized Gompertz growth model with applications and related birth-death processes

2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A. Sajadi ◽  
Serena Spina
Keyword(s):  
Growth Model ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Death Process ◽  
Birth Process ◽  
Failure Data ◽  
First Case ◽  
Gompertz Growth Model ◽  
Birth Death

AbstractIn this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

scholarly journals The Sampling Distribution of Disease-Associated Alleles

Genetics ◽  
1997 ◽  
Vol 147 (4) ◽  
pp. 1855-1861 ◽  
Author(s):  
Montgomery Slatkin ◽  
Bruce Rannala
Keyword(s):  
Low Frequency ◽  
Null Model ◽  
Sampling Distribution ◽  
Death Process ◽  
Published Data ◽  
Data Sets ◽  
Likelihood Functions ◽  
Alternative Hypotheses ◽  
Size Standard ◽  
Birth Death

Abstract A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.

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