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Asymptotic behaviour of d-variate absorption distributions, d = 1, 2


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[1] C. A. Charalambides, Discrete q-distributions on Bernoulli trials with geometrically varying success probability, J. Statist. Plann. Inference, 140 (2010) 2355–2383. Search in Google Scholar

[2] C. A. Charalambides, A q-Pólya urn model and the q-Pólya and the inverse q-Pólya distributions, J. Statist. Plann. Inference, 142 (2012) 276–288. Search in Google Scholar

[3] C. A. Charalambides, On the distributions of absorbed particles in crossing a field containing absorption distributions, Fund. Inform., 117 (2012), 147–154. Search in Google Scholar

[4] C. A. Charalambides, Discrete q-Distributions, John Wiley Sons, New Jersey, 2016.10.1002/9781119119128 Search in Google Scholar

[5] C. A. Charalambides, q-multinomial and negative q-multinomial distributions, Comm. Statist. Theory Methods, 50 (2021) 5673–5898. Search in Google Scholar

[6] C. A. Charalambides, Multivariate q-Pólya and inverse q-Pólya distributions, Comm. Statist. Theory Methods, to appear. Search in Google Scholar

[7] A. W. Kemp and J. Newton, Certain state-dependent processes for dichotomized parasite populations, J. Appl. Probab., 27 (1990) 251–258. Search in Google Scholar

[8] A. W. Kemp, Heine–Euler extensions of the Poisson distribution, Comm. Statist. Theory Methods, 21 (1992) 571–588. Search in Google Scholar

[9] A. W. Kemp, Steady-state Markov chain models for the Heine and Euler distributions, J. Appl. Probab., 29 (1992) 869–876. Search in Google Scholar

[10] A. W. Kemp, Steady-state Markov chain models for certain q-confluent hypergeometric distributions, J. Statist. Plann. Inference, 135 (2005) 107–120. Search in Google Scholar

[11] A. Kyriakoussis and M. G. Vamvakari, q-discrete distributions based on q-Meixner and q-Charlier orthogonal polynomials–Asymptotic behaviour, J. Statist. Plann. Inference, 140 (2010) 2285–2294. Search in Google Scholar

[12] A. Kyriakoussis and M. G. Vamvakari, On a q-analogue of the Stirling formula and a continuous limiting behaviour of the q-binomial distribution–Numerical calculations, Methodol. Comput. Appl. Probab., 15 (2013) 187–213. Search in Google Scholar

[13] A. Kyriakoussis and M. G. Vamvakari, Continuous Stieltjes–Wigert limiting behaviour of a family of confluent q-Chu-Vandermonde distributions, Axioms, 3 (2014), 140–152.10.3390/axioms3020140 Search in Google Scholar

[14] A. Kyriakoussis and M. G. Vamvakari, Heine process as a q-analog of the Poisson process– waiting and interarrival times, Comm. Statist. Theory Methods, 46 (2017) 4088–4102. Search in Google Scholar

[15] A. Kyriakoussis and M. G. Vamvakari, Asymptotic behaviour of certain q-Poisson, q-binomial and negative q-binomial distributions, in: Andrews, G. E., Krattenthaler, C., Krinik, A. (Eds.), Lattice Path Combinatorics and Applications, Developments in Mathematics 58, Springer Nature, Switzerland AG, 2019.10.1007/978-3-030-11102-1_13 Search in Google Scholar

[16] M. G. Vamvakari, On continuous limiting behaviour for the q(n)-binomial distribution with q(n) 1 as n → ∞, Appl. Math., 3 (2012) 2101–2108.10.4236/am.2012.312A290 Search in Google Scholar

[17] M. G. Vamvakari, On multivariate discrete q-distributions–A multivariate q-Cauchy’s formula, Comm. Statist. Theory Methods, 49 (2020) 6080–6095.10.1080/03610926.2019.1626427 Search in Google Scholar