Abstract
The paper defines two modified q-Bessel functions and uses their properties in the study of the distribution of the differences of (i) two Euler variables, (ii) two Heine variables (these are q-analogues of Poisson variables); three-term recurrence relations for the probabilities are obtained and the logcon-cavity of the distributions is established. A particular case of (ii) is the bilateral discrete normal distribution—this involves Jacobi’s triple product. The Euler and the Heine distributions are both special cases of the generalized Euler distribution. The difference of two generalized Euler variables is discussed briefly; other special cases lead to Ramanujan’s 1ψ1 sum and to its finite form.
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© 1997 Birkhäuser Boston
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Kemp, A.W. (1997). On Modified q-Bessel Functions and Some Statistical Applications. In: Balakrishnan, N. (eds) Advances in Combinatorial Methods and Applications to Probability and Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4140-9_27
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DOI: https://doi.org/10.1007/978-1-4612-4140-9_27
Publisher Name: Birkhäuser Boston
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