THERMAL SCIENCE

International Scientific Journal

DISCRETIZATION OF THE METHOD OF GENERATING AN EXPANDED FAMILY OF DISTRIBUTIONS BASED UPON TRUNCATED DISTRIBUTIONS

ABSTRACT
Discretization translates the continuous functions into discrete version making them more adaptable for numerical computation and application in applied mathematics and computer sciences. In this article, discrete analogues of a generalization method of generating a new family of distributions is provided. Several new discrete distributions are derived using the proposed methodology. A discrete Weibull-Geometric distribution is considered and various of its significant characteristics including moment, survival function, reliability function, quantile function, and order statistics are discussed. The method of maximum likelihood and the method of moments are used to estimate the model parameters. The performance of the proposed model is probed through a real data set. A comparison of our model with some existing models is also given to demonstrate its efficiency.
KEYWORDS
PAPER SUBMITTED: 2020-05-05
PAPER REVISED: 2020-11-09
PAPER ACCEPTED: 2020-11-12
PUBLISHED ONLINE: 2021-01-24
DOI REFERENCE: https://doi.org/10.2298/TSCI200605003F
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 1, PAGES [19 - 30]
REFERENCES
  1. Pitman, E. J. G., Some Basic Theory for Statistical Inference: Monographs on Applied Probability and Statistics, CRC Press, Boka Raton, Fla., USA, 2018
  2. Bracquemond, C., Gaudoin, O., A Survey on Discrete Lifetime Distributions, International Journal of Reliability, Quality and Safety Engineering, 10 (2003), 03, pp. 69-98
  3. Dilip, R., The Discrete Normal Distribution, Communications in Statistics-theory and Methods, 32 (2003), 03, pp. 1871-1883
  4. Dilip, R., Discrete Rayleigh Distribution, IEEE Transactions on Reliability, 53 (2004), 02, pp. 255-260
  5. Inusah, S., Kozubowski, T. J., A Discrete Analogue of the Laplace Distribution, Journal of Statistical Planning and Inference, 136 (2006), 03, pp. 1090-1102
  6. Kemp, A. W., Characterizations of a Discrete Normal Distribution, Journal of Statistical Planning and Inference, 63 (1997), 02, pp. 223-229
  7. Alzaatreh, A., et al., On the Discrete Analogues of Continuous Distributions, Statistical Methodology, 9 (2012), 06, pp. 589-603
  8. Alzaatreh, A., et al., A New Method for Generating Families of Continuous Distributions, Metron, 71 (2013), 1, pp. 63-79
  9. Al-Masoud, T. A., A Discrete General Class of Continuous Distributions, M. Sc. thesis, King Abdul Aziz University, Jeddah, Saudi Arabia Kingdom, 2013
  10. Almalki, S. J., Nadarajah, S., A New Discrete Modified Weibull Distribution, IEEE Transactions on Reliability, 63 (2014), 1, pp. 68-80
  11. Nekoukhou, V., Bidram, H., The Exponentiated Discrete Weibull Distribution, SORT, 39 (2015), 1, pp. 127-146
  12. Hossain, M. S., On a Family of Discrete Probability Distributions (FDPD), European Journal of Statistics and Probability, 4 (2016), 5, pp. 1-10
  13. Alamatsaz, M. H., et al., Discrete Generalized Rayleigh Distribution, Pakistan Journal of Statistics, 32 (2016), 1, pp. 1-20
  14. Chakraborty, S., Generating Discrete Analogues of Continuous Probability Distributions – A Survey of Methods and Constructions, Journal of Statistical Distributions and Applications, 2 (2015), 1, 6
  15. Chakraborty, S., Chakravarty, D., A New Discrete Probability Distribution with Integer Support on, Communications in Statistics-Theory and Methods, 45 (2016), 2, pp. 492-505
  16. Jayakumar, K., Babu, M. G., Discrete Weibull Geometric Distribution and Its Properties, Communications in Statistics-Theory and Methods, 47 (2018), 7, pp. 1767-1783
  17. Mazucheli, J., et al., Two Useful Discrete Distributions to Model Overdispersed Count Data, Revista Colombiana de Estadistica, 43 (2020), 1, pp. 21-48
  18. Keilson, J., Gerber, H., Some Results for Discrete Unimodality, Journal of the American Statistical Association, 66 (1971), 334, pp. 386-389
  19. Para, B. A., Jan, T. R., On Discrete Three Parameter Burr Type xii and Discrete Lomax Distributions and Their Applications to Model Count Data from Medical Science, Biometrics and Biostatistics International Journal, 4 (2016), 2, pp. 71-82
  20. Chan, A.-K., et al., Corticosteroid-Induced Kidney Dysmorphogenesis is Associated with Deregulated Expression of Known Cystogenic Molecules, as Well as Indian Hedgehog, American Journal of Physiology-Renal Physiology, 298 (2009), 2, pp. F346-F356

© 2021 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence