Generalized Pareto distribution based on generalized order statistics and associated inference

Mansoor Rashid Malik; Devendra Kumar

doi:10.21307/stattrans-2019-024

Generalized Pareto distribution based on generalized order statistics and associated inference

Mansoor Rashid Malik , Devendra Kumar Department of Statistics, Central University of Haryana, Mahendergarh, India ORCID:https://orcid.org/0000-0001-5831-3315 Statistics in Transition new series, vol. 20, 2019, 3, pages: 57-79 Published online: 30 August 2019 DOI 10.21307/stattrans-2019-024

1086 Views 37 Downloads

ARTICLE

(English) PDF

ABSTRACT

In this paper, we have considered the generalized Pareto distribution. Various structural properties of the distribution are derived including (quantile function, explicit expressions for moments, mean deviation, Bonferroni and Lorenz curves and Renyi entropy). We have provided simple explicit expressions and recurrence relations for single and product moments of generalized order statistics from the generalized Pareto distribution. The method of maximum likelihood is adopted for estimating the model parameters. For different parameter settings and sample sizes, the simulation studies are performed and compared to the performance of the generalized Pareto distribution.

KEYWORDS

generalized order statistics, generalized Pareto distribution, single and product moment, recurrence relations, characterization and maximum likelihood estimation

REFERENCES

ABOELENEEN, Z. A., (2010). Inference for Weibull distribution under generalized order statistics, Mathematics and Computers in Simulation, 8, pp. 26–36.

ARNOLD, B. C., (1983). The Pareto distribution, International Co-operative Publishing Houshing, Fairland, MD.

ARNOLD, B. C. (2008). Pareto and Generalized Pareto Distributions. In: Chotikapanich D. (eds.) Modeling Income Distributions and Lorenz Curves. Economic Studies in Equality, Social Exclusion and Well-Being, vol. 5 , Springer, New York, NY.

BONFERRONI C. E., (1930). Elmenti di statistica generale, Libreria Seber, Firenze.

BURKSHAT, M., (2010). Linear estimators and predictors based on generalized order statistics from generalized Pareto distributions, Comm. Statist. Theory Methords, 39 , pp. 311–326.

Gradshteyn, I. S., Ryzhik, I.M., (2014). Table of Integrals, Series, and Products. Sixth edition, San Diego: Academic Press.

KAMPS, U., (1995). A concept of generalized order statistics, B.G. Teubner Stuttgart, Germany .

KENNEY, J. F., KEEPIN, E., (1962). Mathematics of Statistics, D. Van Nostrand Company.

KIM, C., HAN, K., (2014). Bayesian estimation of Rayleigh distribution based on generalized order statistics, Applied Mathematics Sciences, 8, pp. 7475– 7485.

KUMAR, D., (2015a). The extended generalized half logistic distribution based on ordered random variables, Tamkang Journal of Mathematics, 46, pp. 245– 256.

KUMAR, D., (2015b). Exact moments of generalized order statistics from type II exponentiated log-logistic distribution, Hacettepe Journal of Mathematics and Statistics, 44, pp. 715–733.

KUMAR, D., DEY, S., (2017a). Relations for moments of generalized order statistics from extended exponential distribution, American Journal of Mathematical and Management Sciences, 17, pp. 378–400.

KUMAR, D., DEY, S., (2017b). Power generalized Weibull distribution based on order statistics, Journal of Statistical Research, 51, pp. 61–78.

KUMAR, D., DEY, S., NADARAJAH, S., (2017). Extended exponential distribution based on order statistics, Communication in Statistics-Theory and Methods, 46, pp. 9166–9184.

KUMAR, D., JAIN N. (2018). Power generalized Weibull distribution based on generalised order statistics, Journal of data Science, 16, pp. 621–646.

KUMAR, D., GOYAL, A., (2019a). Order Statistics from the Power Lindley Distribution and Associated Inference with Application, Annals of Data Sciences, 6, pp. 153–177.

KUMAR, D., GOYAL, A., (2019b). Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application, Annals of Data Sciences, https://doi.org/10.1007/s40745-019-00196-6.

LAWLESS, J. F., (1982). Statistical models and methods for lifetime data, 2nd Edition, Wiley, New York.

MOORS, J. J. A., (1988). A quantile alternative for kurtosis, Journal of the Royal Statistical Society. Series D (The Statistician), 37, pp. 25–32.

PICKANDS, J., (1975). Statistical inference using extreme order statistics, Ann. Statist. 3, pp. 119–131.

SAFI, S. K., AHMED, R. H., (2013). Statistical estimation based on generalized order statistics from Kumaraswamy distribution, Proceeding of the 14st Applied Stochastic Models and Data Analysis (ASMDA) International Conference, Mataro (Barcelona), Spain, pp. 25–28.

Verma, V., Betti, G., (2006). EU Statistics on Income and Living Conditions (EUSILC): Choosing the Survey Structure and Sample Design, Statistics in Transition, 7, pp. 935–970.

WU, S. J., CHEN, Y. J., CHANG, C. T., (2014). Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution, Journal of Statistical Computation and Simulations, 77, pp. 19–27.