caa a22 4500 47706292X CHVBK 20180405111406.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF00052333 doi (NATIONALLICENCE)springer-10.1007/BF00052333 Koutras M. Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Greece aut On a waiting time distribution in a sequence of Bernoulli trials [Elektronische Daten] [M. Koutras] In the present article we investigate the exact distribution of the waiting time for the r-th non-overlapping appearance of a pair of successes separated by at mosk k−2 failures (k≥2) in a sequence of independent and identically distributed (iid) Bernoulli trials. Formulae are provided for the probability distribution function, probability generating function and moments and some asymptotic results are discussed. Expressions in terms of certain generalised Fibonacci numbers and polynomials are also included. The Institute of Statistical Mathematics, 1996 Waiting times nationallicence success runs nationallicence scans nationallicence distributions of order k nationallicence Fibonacci numbers nationallicence unimodality nationallicence Markov dependence nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 789-806 0020-3157 48:4<789 1996 48 10463 https://doi.org/10.1007/BF00052333 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00052333 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Koutras M. Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Greece aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 789-806 0020-3157 48:4<789 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer