Abd Anasir EDABAAGöksal BİLGİCİ2023-04-142023-04-142021-01-01Edabaa, A., Bi̇lgi̇ci̇, G. (2021). On waiting time distribution of runs in a Fibonacci and Lucassequences. Avrupa Bilim ve Teknoloji Dergisi, 0(25), 774-781https://search.trdizin.gov.tr/publication/detail/466608/on-waiting-time-distribution-of-runs-in-a-fibonacci-and-lucassequenceshttps://hdl.handle.net/20.500.12597/6717There is an increasingly needed to development a new mathematical apparatus concerned with the description, prediction, andunderstanding of natural phenomena in a precise manner. The purpose of this study is to extend the mathematical framework ofFibonacci and Lucas sequences for underpinned and establishing a modern mathematical formulas. For this purpose, we deriveanalytical formulas of order k-Fibonacci and order k-Lucas sequences simultaneously based on Bernoulli sequence. Furthermore,exploiting a relationship with the k th order Fibonacci and Lucas sequence, we study the probability distribution function (pdf) of thewaiting time (W (k)).enginfo:eu-repo/semantics/openAccessRESEARCH10.31590/ejosat.7827904666087747810252148-2683