VACCINATION: ITS BIRTH, DEATH AND RESURRECTION EIGHTH BURNET LECTURE OF THE AUSTRALIAN ACADEMY OF SCIENCE, 1985

1985 ◽  
Vol 63 (6) ◽  
pp. 607-622 ◽  
Author(s):  
Frank Fenner
Keyword(s):  
Australian Academy ◽  
Birth Death

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.

SHORT OR LONG FUSE: TIMING THE ORDOVICIAN RADIATION USING THE FOSSILIZED BIRTH DEATH MODEL

2017 ◽  
Author(s):  
Curtis R. Congreve ◽  
◽  
Peter J. Wagner ◽  
Mark E. Patzkowsky
Keyword(s):  
Birth Death

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 Non-local Solvable Birth–Death Processes

2021 ◽  
Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Limit Distribution ◽  
Spectral Decomposition ◽  
Strong Solutions ◽  
Stochastic Representation ◽  
Discrete Approximations ◽  
Local Difference ◽  
Non Local ◽  
Birth Death

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

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.

scholarly journals Light People: Professor Chennupati Jagadish

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Hui Wang
Keyword(s):  
Developing Countries ◽  
Scientific Research ◽  
Educational Opportunities ◽  
Research Career ◽  
National University ◽  
Education In India ◽  
Set Up ◽  
Equal Educational Opportunities ◽  
Australian Academy ◽  
Young Researchers

EditorialIn 2018, the Indian film “Starting Line” focused the public’s attention on the issue of education in India. It depicted the length some Indian parents were willing to go to secure educational resources for their children, as well as the difficulties faced by those disadvantaged in society in their fight for equal educational opportunities. In reality, many brilliant young Indian talents have been able to study in Australia through a fund set up by Prof. Chennupati Jagadish, a Distinguished Professor of the Australian National University. Prof. Jagadish is a Fellow of the Australian Academy of Science and the Australian Academy of Technological Sciences and Engineering. In 2018 he was awarded a UNESCO Prize for his contribution to the development of nanoscience and nanotechnology. He holds many positions, and has won numerous awards. What started Prof. Jagadish on his scientific research career? How did he become the respected scientist he is today? What was his intention in setting up the educational fund for students from developing countries? What advice does he have for young researchers? Here are the answers from Prof. Jagadish.

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