THE MODIFIED RANDOM WALK DISTRIBUTION
Keywords:
Lagrange, Over-dispersion, Under-dispersion, Unimodal
Abstract
This study presents a modification to a two-parameter distribution, yielding a discrete distribution termed the modified random walk distribution. This modification is derived from the random walk distribution and falls within the family of Lagrangian probability distributions. Comprehensive investigations are conducted on both the random walk distribution and its modified counterpart to discern and analyze their respective properties. Furthermore, a recursive formula for generating probabilities associated with this distribution is proposed. This research contributes to the understanding of the random walk distribution and provides insights into the implications of its modification.
References
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[14] G. F. Lawler, V. Limic. Random Walk: A Modern Introduction (Cambridge studies in Advance Mathematics) Cambridge University Press, Cambridge, England (2010).
[15] R. Maity. Probability Distributions and Their Applications. Springer Transactions in Civil and Environmental Engineering, (2018). 93–143. doi:10.1007/978-981-10-8779-0_4
[16] J. C. Tanner. A derivation of the Borel distribution. Biometrika, (48), (1961) 222-224.
[17] J. C. Tanner. A problem of interference between two queues. Biometrika, (40), (1953) 58-69.
[18] G. H. Weiss, S. Havlin. Some properties of a random walk on a comb structure, Physica A: Statistical Mechanics and its Applications, Volume 134, Issue 2, (1986) Pages 474-482
[19] F. Xia, J. Liu, H. Nie, Y. Fu, L. Wan, X. Kong. Random Walks: A Review of Algorithms and Applications. IEEE Transactions on Emerging Topics in Computational Intelligence, (2019). 1–13. doi:10.1109/tetci.2019.2952908
[20] A. Zahoor, R. Adil, T. R. Jan. A new discrete compound distribution with application. Journal of Statistics Applications and Probability 6(1) (2017) 233-241.
[2] A. Bhattacharyya, J. Mitra, S. Bhattacharyya. A Brief Study on Simple Random Walk in 1D. Reson 28, (2023) 945–958 https://doi.org/10.1007/s12045-023-1624-2
[3] E. Borel. Surl’ employ du theorem de Bernoulli pour faci liter, le calcul d’ un infinite de coefficients. Application un problem de l’ attente a un guichet. Comptes Rendus Academie des Sciences, Paris Series A, (214), (1942) 452-456.
[4] P. C. Consul, F. Famoye. Lagrangian Probability Distributions. Birkhauser, Boston, USA, (2006).
[5] P.C. Consul, L.R. Shenton. On the probabilistic structure and properties of discrete Lagrangian distributions. A modern course on Statistical Distributions in Scientific work, D. Riedel, Boston, M.A1, (1975) 41-57.
[6] F. Famoye. Generalized geometric distribution and some applications. Journal of Mathematical Sciences (8), (1997a) 1-13.
[7] R. P. Gupta, G. C. Jain. A bivariate Borel-Tanner distribution and its approximations. Journal of Statistical Computation and Simulation. 6(2) (1977) 129-135.
[8] R.P. Gupta, G.C. Jain. Some applications of a bivariate Borel-Tanner distribution. Biometrical Journal. 20(2) (1978) 99-105.
[9] A. Hills. Random walks: The Properties, Applications and Methods of Analysis. Bachelor’s Thesis, University of Groningen, Groningen Netherlands (2020).
[10] Z. Hossein, F. Pouya, N. Ismail. Bivariate generalized Poisson regression model: Applications on health care data. Empirical Economics, Journal of the Institute for Advanced Studies. 51(4), (2016) 1607-1621.
[11] T. Imoto. Properties of Lagrangian distribution. Communications in Statistics-Theory and Methods, 45(3) (2016) 712-721.
[12] M. N. Islam, P. C Consul. The Consul distribution as a bunching model in traffic flow. Transportation Research Part B: Methodological. (25), (1990) 365-372.
[13] N. C. Jain, & S. Orey, Some properties of random walk paths. Journal of Mathematical Analysis and Applications, 43(3), (1973) 795– 815. doi:10.1016/0022- 247x(73)90293-x
[14] G. F. Lawler, V. Limic. Random Walk: A Modern Introduction (Cambridge studies in Advance Mathematics) Cambridge University Press, Cambridge, England (2010).
[15] R. Maity. Probability Distributions and Their Applications. Springer Transactions in Civil and Environmental Engineering, (2018). 93–143. doi:10.1007/978-981-10-8779-0_4
[16] J. C. Tanner. A derivation of the Borel distribution. Biometrika, (48), (1961) 222-224.
[17] J. C. Tanner. A problem of interference between two queues. Biometrika, (40), (1953) 58-69.
[18] G. H. Weiss, S. Havlin. Some properties of a random walk on a comb structure, Physica A: Statistical Mechanics and its Applications, Volume 134, Issue 2, (1986) Pages 474-482
[19] F. Xia, J. Liu, H. Nie, Y. Fu, L. Wan, X. Kong. Random Walks: A Review of Algorithms and Applications. IEEE Transactions on Emerging Topics in Computational Intelligence, (2019). 1–13. doi:10.1109/tetci.2019.2952908
[20] A. Zahoor, R. Adil, T. R. Jan. A new discrete compound distribution with application. Journal of Statistics Applications and Probability 6(1) (2017) 233-241.
Published
2024-11-30
How to Cite
ADAMU, L., & FAMOYE, F. (2024). THE MODIFIED RANDOM WALK DISTRIBUTION. Unilag Journal of Mathematics and Applications, 4(1), 51-69. Retrieved from http://lagjma.unilag.edu.ng/article/view/2283
Section
Articles
Copyright (c) 2024 LATEEF ADAMU, FELIX FAMOYE
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