A Note on Fibonacci Sequences of Random Variables

Authors

  • Ismihan Bayramoğlu Izmir University of Economics

DOI:

https://doi.org/10.6092/issn.1973-2201/13354

Keywords:

Random variable, Distribution function, Probability density function, Sequence of random variables

Abstract

The aim of this paper is to introduce and investigate the newrandom sequence in the form{X0, X1, Xn = Xn−2 +Xn−1, n = 2, 3, ..˙} , referred to as Fibonacci Sequence of Random Variables (FSRV). The initial random variables X0 and X1 are assumed to be absolutely continuous with joint probability density function (pdf) fX0,X1 . The FSRV is completely determined by X0 and X1 and the members of Fibonacci sequence F ≡ {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...}. We examine the distributional and limit properties of the random sequence Xn, n = 0, 1, 2, ... .

References

L. E. DICKSON (1966). History of the Theory of Numbers. Chelsea Publishing Company, New York.

W. FELLER (1971). An Introduction to Probability Theory and Its Applications. John Wiley & Sons Inc., New York, London, Sydney.

B. GNEDENKO (1978). The Theory of Probability. Mir Publishers, Moscow.

S. ROSS (2016). A First Course in Probability. Prentice-Hall Inc, New Jersey.

A. SKOROKHOD (2005). Basic Principles and Applications of Probability Theory. Springer, Berlin.

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Published

2022-07-12

How to Cite

Bayramoğlu, I. (2022). A Note on Fibonacci Sequences of Random Variables. Statistica, 82(1), 41–55. https://doi.org/10.6092/issn.1973-2201/13354

Issue

Vol. 82 No. 1 (2022)

Section

Articles

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