Discrete New Generalized Pareto Distribution
DOI:
https://doi.org/10.6092/issn.1973-2201/11380Keywords:
Discrete new generalized Pareto distribution, Hazard rate function, Maximum likelihood estimation, Stress-strength reliabilityAbstract
In this paper we propose a discrete analogue of New Generalized Pareto distribution as a new discrete model using general approach of discretization of continuous distribution. The structural properties of the new distribution are discussed. The shape properties, moments, median, infinite divisibility and stress-strength properties are derived. Estimation of parameters are done using maximum likelihood method. An application of real data set shows the suitability of the proposed model.
References
B. C. ARNOLD (2008). Pareto and generalized Pareto distributions. In D. CHOTIKAPANICH (ed.), Modeling Income Distributions and Lorenz Curves, Springer, NewYork, pp. 119–145.
A. BUDDANA, T. J. KOZUBOWSKI (2014). Discrete Pareto distributions. Economic Quality Control, 29, no. 2, pp. 143–156.
S. CHAKRABORTY (2015). Generating discrete analogues of continuous probability distributions-a survey of methods and constructions. Journal of Statistical Distributions and Applications, 2, no. 1, pp. 1–30.
S.CHAKRABORTY, D.CHAKRAVARTY (2012). Discrete gamma distributions: properties and parameter estimation. Communications in Statistics-Theory and Methods, 41, no. 18, pp. 3301–3324.
S. CHAKRABORTY, D. CHAKRAVARTY (2014). A discrete Gumbel distribution. arXiv preprint arXiv:1410.7568.
S. CHAKRABORTY, D. CHAKRAVARTY (2015). A discrete power distribution. arXiv preprint arXiv:1501.06299.
V.CHOULAKIAN, M.A. STEPHENS (2001). Goodness-of-fit tests for the generalized Pareto distribution. Technometrics, 43, no. 4, pp. 478–484.
I. GHOSH (2020). A new discrete Pareto type (IV) model: theory, properties and applications. Journal of Statistical Distributions and Applications, 7, no. 1, pp. 1–17.
S. INUSAH, T. J. KOZUBOWSKI (2006). A discrete analogue of the Laplace distribution. Journal of Statistical Planning and Inference, 136, no. 3, pp. 1090–1102.
K. JAYAKUMAR, B. KRISHNAN, G. HAMEDANI (2020). On a new generalization of Pareto distribution and its applications. Communications in Statistics-Simulation and Computation, 49, no. 5, pp. 1264–1284.
K. JAYAKUMAR, K. K. SANKARAN (2016). On a generalisation of uniform distribution and its properties. Statistica, 76, no. 1, pp. 83–91.
K. JAYAKUMAR, K. K. SANKARAN (2018). A generalization of discrete Weibull distribution. Communications in Statistics-Theory and Methods, 47, no. 24, pp. 6064–6078.
A. W. KEMP (1997). Characterizations of a discrete normal distribution. Journal of Statistical Planning and Inference, 63, no. 2, pp. 223–229.
A. W. KEMP (2008). The discrete half-normal distribution. In Advances in Mathematical and Statistical Modeling, Springer, Birkhäuser Boston., Boston, pp. 353–360.
C. KLÜPPELBERG (1988). Subexponential distributions and integrated tails. Journal of Applied Probability, 25, no. 1, pp. 132–141.
T. J. KOZUBOWSKI, S. INUSAH (2006). A skew Laplace distribution on integers. Annals of the Institute of Statistical Mathematics, 58, no. 3, pp. 555–571.
H. KRISHNA, P. S. PUNDIR (2009). Discrete Burr and discrete Pareto distributions. Statistical Methodology, 6, no. 2, pp. 177–188.
T. NAKAGAWA, S. OSAKI (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24, no. 5, pp. 300–301.
V. NEKOUKHOU, H. BIDRAM (2015). The exponentiated discrete Weibull distribution. Sort, 39, pp. 127–146.
W. PADGETT, J. D. SPURRIER (1985). On discrete failure models. IEEE Transactions on Reliability, 34, no. 3, pp. 253–256.
B. PARA, T. JAN (2016). On discrete three parameter Burr type XII and discrete Lomax distributions and their applications to model count data from medical science. Biometrics & Biostatistics International Journal, 4, no. 2, pp. 1–15.
F. PRIETO, E. GÓMEZ-DÉNIZ, J. M. SARABIA (2014). Modelling road accident blackspots data with the discrete generalized Pareto distribution. Accident Analysis & Prevention, 71, pp. 38– 49.
R CORE TEAM (2013). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/. ISBN 3-900051-07-0.
D. ROY (2003). The discrete normal distribution. Communications in Statistics-Theory and Methods, 32, no. 10, pp. 1871–1883.
H. SATO, M. IKOTA, A. SUGIMOTO, H. MASUDA (1999). A new defect distribution metrology with a consistent discrete exponential formula and its applications. IEEE Transactions on Semiconductor Manufacturing, 12, no. 4, pp. 409–418.
W. E. STEIN, R. DATTERO (1984). A new discrete Weibull distribution. IEEE Transactions on Reliability, 33, no. 2, pp. 196–197.
F. W. STEUTEL, K. VAN HARN (2003). Infinite Divisibility of Probability Distributions on the Real Line. CRC Press, Boca Raton.
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