A Muth-Pareto Distribution: Properties, Estimation, Characterizations and Applications
DOI:
https://doi.org/10.6092/issn.1973-2201/12760Keywords:
Characterizations, Estimation, Muth-Pareto distribution, Order statistics , Truncated moment, Upper record valuesAbstract
In this paper, a new distribution of the Muth-generated family is introduced by considering the Pareto model as baseline with the goal of having increased flexibility and improved goodness of fit in terms of studying tail characteristics. Maximum likelihood estimated parameters of the distribution were found to be consistent and asymptotically unbiased. From a practical point of view, it is shown that the proposed distribution is more flexible than some common statistical distributions. In particular, the proposed model proved to fit well into unimodal data structures. Some mathematical properties were derived, and characterization investigated by truncated first moment where a product of reverse hazard rate and another function of the truncated point is considered. Other characterizations by order statistics and upper record values based on the characterization by the first truncated moment were also established.
References
M. AHSANULLAH (1995). Record Statistics. Nova Science Publishers, New York, USA.
M. AHSANULLAH (2017). Characterizations of Univariate Continuous Distributions. Atlantis-Press, Paris, France.
M.AHSANULLAH, B.KIBRIA, M. SHAKIL (2014). Normal and Student´s t-Distributions and their Applications. Atlantis-Press, Paris, France.
M.AHSANULLAH, V.NEVZOROV, M. SHAKIL (2013). An Introduction to Order Statistics. Atlantis-Press, Paris, France.
M. AHSANULLAH, M. SHAKIL, B. KIBRIA (2015). Characterizations of folded Student’s t-distribution. Journal of Statistical Distributions and Applications, 2, no. 1, p. 15.
A.ALMARASHI, M. ELGARHY (2018). Anewmuth-generated family of distributions with applications. Journal of Nonlinear Sciences and Applications, 11, no. 1, pp. 1171–1184.
A. ALZAATREH, C. LEE, F. FAMOYE (2013). A new method for generating families of continuous distributions. Metron, 71, no. 1,2, p. 63–79.
B. ARNOLD, BALAKRISHNAN, H. NAGARAJA (2005). First Course in Order Statistics. Wiley, New York, USA.
M. BOURGUIGNON, R. S. B, L. ZEA, G. CORDEIRO (2012). The kumaraswamy pareto distribution. Statistical Methods, 42, pp. 1–20.
M. BOURGUIGNON, R. SILVA, G. CORDEIRO (2014). The Weibull-G family of probability distributions. Journal of Data Science, 12, no. 1, p. 53–68.
R. CORLESS, G. GONNET, D. HARE, D. JEFFREY, D. KNUTH (1996). On the lambert w function. Advances in Computational Mathematics, 5, no. 4, pp. 329–359.
H. DAVID, H. NAGARAJA (2003). Order Statistics, Third Edition. Wiley, New York, USA.
N. EUGENE, C. LEE, F. FAMOYE (2002). Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31, no. 1, p. 497–512.
J.GALAMBOS, S.KOTZ (2006). Characterizations of Probability Distributions.: A Unified Approach with an Emphasis on Exponential and Related Models., vol. 675. Springer-Verlag, Berlin.
W. GLÄNZEL (1987). A characterization theorem based on truncated moments and its application to some distribution families. In P. BAUER, F. KONECNY,W.WERTZ (eds.), Mathematical Statistics and Probability Theory, Springer Netherlands, Dordrecht, pp. 75–84.
W. GLANZEL (1990). Some consequences of a characterization theorem based on truncated moments. Statistics, 21, no. 4, pp. 613–618.
W.GLÄNZEL, A. TELES, A. SCHUBERT (1984). Characterization by truncated moments and its application to pearson-type distributions. Zeitschrift fürWahrscheinlichkeitstheorie und verwandte Gebiete, 66, no. 2, pp. 173–183.
P. JODRÁ, H. GOMEZ, M. JIMÉNEZ-GAMERO, M. ALBA-FERNÁNDEZ (2017). The power muth distribution. Mathematical Modelling and Analysis, 22, no. 2, pp. 186–201.
P. JODRÁ, M. D. JIMÉNEZ GAMERO, M. V. ALBA FERNÁNDEZ (2015). On the muth distribution. Mathematical Modelling and Analysis, 20, no. 3, pp. 291–310.
A. KAREEMA, M. BOSHI (2013). Exponential pareto distribution. Mathemetical Theory and Modeling, 3, no. 5, pp. 135–146.
S. KOTZ, D. SHANBHAG (1980). Some new approaches to probability distributions. Advances in Applied Probability, 12, no. 4, pp. 903–921.
L. LEEMIS, J.MCQUESTON (2008). Univariate distribution relationships. The American Statistician, 62, no. 1, pp. 45–53.
M. MEAD (2014). Extended pareto distribution. Pakistan Journal of Statistics and Operations Research, 10, no. 3, pp. 313–329.
B. MILOŠEVIC (2017). Some recent characterization based goodness of fit tests. In T.WIKLUND (ed.), the Proceedings of the 20th European Young Statisticians Meeting. pp. 67–73.
MUSADDIQ SIRAJO (2020). Generalization of Muth Distribution with It’s Properties and Applications. An MSc Dissertation of Department of Statistics, Ahmadu Bello University,Zaria-Nigeria.
E. J.MUTH (1977). Reliability models with positive memory derived from the mean residual life function. In C. P. TSOKOS, I. N. SHIMI (eds.), Theory and applications of reliability, Academic Press, pp. 410–434.
H. NAGARAJA (2006). Characterizations of probability distributions. In H. PHAM (ed.), Springer Handbook of Engineering Statistics, Springer, London, pp. 79–95.
M.NASSAR, N.NADA (2011). The beta generalized pareto distribution. Journal of statistics: Advances in Theory and Applications, 6, no. 1, pp. 1–17.
J. NELDER, R. MEAD (1965). A simplex method for function minimization. Computer Journal, 7, pp. 308–313.
V. B. NEVZOROV (2001). Records: mathematical theory. American Mathematical Society.
Y.Y.NIKITIN (2017). Tests based on characterizations, and their efficiencies: a survey. Acta et Commentationes Universitatis Tartuensis de Mathematica, 21, no. 1, pp. 3–24.
F. PROSCHAN (1963). Theoretical explanation of observed decreasing failure rate. Technometrics, 5, no. 1, pp. 375–383.
R CORE TEAM (2021). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.
M. SHAKIL, M. AHSANULLAH, B. G. KIBRIA (2018). On the characterizations of chen’s two-parameter exponential power life-testing distribution. Journal of Statistical Theory and Applications, 17, no. 3, pp. 393–407.
M. H. TAHIR, G. M. CORDEIRO, S. ALI, S. DEY, A. MANZOOR (2018). The inverted nadarajah–haghighi distribution: estimation methods and applications. Journal of Statistical Computation and Simulation, 88, no. 14, pp. 2775–2798.
K. Y. VOLKOVA, Y. Y. NIKITIN (2015). Exponentiality tests based on ahsanullah’s characterization and their efficiency. Journal of Mathematical Sciences, 204, no. 1, pp. 42–54.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
