Abstract
Overlapping coefficient is a direct measure of similarity between two distributions which is recently becoming very useful. This paper investigates estimation for some well-known measures of overlap, namely Matusita’s measure ρ, Weitzman’s measure Δ and Λ based on Kullback–Leibler. Two estimation methods considered in this study are point estimation and Bayesian approach. Two inverse Lomax populations with different shape parameters are considered. The bias and mean square error properties of the estimators are studied through a simulation study and a real data example.
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References
C. Kleiber, S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley & Sons, 2003, p. 470.
D. McKenzie, C. Miller, D.A. Falk, The Landscape Ecology of Fire, Springer Science & Business Media, Dordrecht, Netherlands, 2011.
K. Matusita, Ann. Math. Stat. 26 (1955), 631–640.
M.S. Weitzman, Measures of Overlap of Income Distributions of White and Negro Families in the United States, US Bureau of the Census, 1970, p. 22.
S. Kullback, R.A. Leibler, Ann. Math. Stat. 22 (1951), 79–86.
E.P. Smith, Ecology. 63 (1982), 1675–1681.
S.N. Mishra, A.K. Shah, J.J. Lefante, Commun. Stat. Theory Methods. 15 (1986), 123–128.
O. Al-Saidy, H.M. Samawi, M.F. Al-Saleh, ESAIM: Probab. Stat. 9 (2005), 206–219.
T.E. Clemons, The Overlapping Coefficient for Two Normal Probability Functions with Unequal Variances, Dissertation, University of Alabama at Birmingham, School of Joint Health Sciences, Birmingham, AL, USA, 1996.
H. Dhaker, P. Ngom, B. Ibrahimouf, M. Mbodj, J. Math. Res. 2 (2019), 114–124.
H.F. Inman, E.L. Bradley Jr., Commun. Stat. Theory Methods. 18 (1989), 3851–3874.
S. Jose, S. Thomas, T. Mathew, J. Stat. Theory Appl. 18 (2019), 26–32.
M.S. Mulekar, S.N. Mishra, J. Japan Stat. Soc. 24 (1994), 169–180.
B. Reiser, D. Faraggi, J. R. Stat. Soc. Ser. D Stat. 48 (1999), 413–418.
G.A. McIntyre, Aust. J. Agric. Res. 3 (1952), 385–390.
A. Helu, H. Samawi, J. Stat. Theory Pract. 5 (2011), 683–696.
U. Jan, S.P. Ahmad, Bayesian Anal. 7 (2017), 1–12.
A.S. Yadav, S.K. Singh, U. Singh, Statistica. 76 (2016), 185–203.
F. Proschan, Technometrics. 42 (2000), 7–11.
R.C. Gupta, M.E. Ghitany, D.K. Al-Mutairi, J. Stat. Comput. Simul. 80 (2010), 937–947.
M. Saleem, M. Aslam, Pak. J. Stat. 25 (2009), 71–82.
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Dhaker, H., Deme, E.H. & El-Adlouni, S. On Inference of Overlapping Coefficients in Two Inverse Lomax Populations. J Stat Theory Appl 20, 61–75 (2021). https://doi.org/10.2991/jsta.d.210107.002
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DOI: https://doi.org/10.2991/jsta.d.210107.002