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Inference on Overlapping Coefficients in Two Exponential Populations Using Ranked Set Sampling
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 Title & Authors
Inference on Overlapping Coefficients in Two Exponential Populations Using Ranked Set Sampling
Samawi, Hani M.; Al-Saleh, Mohammad F.;
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 Abstract
We consider using ranked set sampling methods to draw inference about the three well-known measures of overlap, namely Matusita`s measure , Morisita`s measure and Weitzman`s measure . Two exponential populations with different means are considered. Due to the difficulties of calculating the precision or the bias of the resulting estimators of overlap measures, because there are no closed-form exact formulas for their variances and their exact sampling distributions, Monte Carlo evaluations are used. Confidence intervals for those measures are also constructed via the bootstrap method and Taylor series approximation.
 Keywords
Bootstrap method;Matusita`s measure;Morisita`s measure;overlap coefficients;Taylor expansion;Weitzman`s measure;ranked set sampling;
 Language
English
 Cited by
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Journal of the Korean Data Analysis Society, 2010. vol.12. 1, pp.83-93
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Nonparametric overlap coefficient estimation using ranked set sampling, Journal of Nonparametric Statistics, 2011, 23, 2, 385  crossref(new windwow)
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On Inference of Overlapping Coefficients in TwoLomaxPopulations Using Different Sampling Methods, Journal of Statistical Theory and Practice, 2011, 5, 4, 683  crossref(new windwow)
 References
1.
Al-Saleh, M. F. and Al-Kadiri, M. A. (2000). Double-ranked set sampling. Statistics & Probability Letters, 48, 205-212 crossref(new window)

2.
Al-Saleh, M. F. and Al-Omari, A. I. (2002). Multistage ranked set sampling. Journal of Statistical Planning and Inference, 102, 273-286 crossref(new window)

3.
Al-Saleh, M. F. and Samawi, H. M. (2006). Inference on overlapping coefficients in two exponential populations. Submitted for publication

4.
Al-Saidy, O., Samawi H. M. and Al-Saleh, M. F. (2005). Inference on overlap coefficients under the weibull distribution: Equal shape parameter. ESAIM: Probability and Statistics, 9, 206-219 crossref(new window)

5.
Bradley, E. L. and Piantadosi, S. (1982). The overlapping coefficient as a measure of agreement between distributions. Technical Report, Department of Biostatistics and Biomathematics, University of Alabama at Birmingham, Birmingham, AL

6.
Clemons, T. E. (1996). The overlapping coefficient for two normal probability functions with unequal variances. Unpublished Thesis, Department of Biostatistics, Univer- sity of Alabama at Birmingham, Birmingham, AL

7.
Clemons, T. E. and Bradley, E. L. (2000). A nonparametric measure of the overlapping coefficient. Computational Statistics & Data Analysis, 34, 51-61 crossref(new window)

8.
Dixon, P. M. (1993). The bootstrap and the jackknife: Describing the precision of ecological indices. Design and Analysis of Ecological Experiments (Scheiner, S. M. and Gurevitch J., eds.), 290-318, Chapman & Hall, New York.

9.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7, 1-26 crossref(new window)

10.
Federer, W. T., Powers, L. R. and Payne, M. G. (1963). Studies on statistical procedures applied to chemical genetic data from sugar beets. Technical Bulletin, 77, Agricultural Experimentation Station, Colorado State University

11.
Harner, E. J. and Whitmore, R. C. (1977). Multivariate measures of niche overlap using discriminant analysis. Theoretical Population Biology, 12, 21-36 crossref(new window)

12.
Hui, T. P., Modarres, R. and Zheng, G. (2005). Bootstrap confidence interval esti- mation of mean via ranked set sampling linear regression. Journal of Statistical Computation and Simulation, 75, 543-553 crossref(new window)

13.
Ibrahim, H. I. (1991). Evaluating the power of the Mann-Whitney test using the boot- strap method. Communications in Statistics-Theory and Methods, 20, 2919-2931 crossref(new window)

14.
Ichikawa, M. (1993). A meaning of the overlapped area under probability density curves of stress and strength. Reliability Engineering & System Safety, 41, 203-204 crossref(new window)

15.
Inman, H. F. and Bradley, E. L. (1989). The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Communications in Statistics-Theory and Methods, 18, 3851-3874 crossref(new window)

16.
Kaur, A., Patil, G. P., Sinha, A. K. and Tailie, C. (1995). Ranked set sampling: An annotated bibliography. Environmental and Ecological Statistics, 2, 25-54 crossref(new window)

17.
Lu, R. P., Smith, E. P. and Good, I. J. (1989). Multivariate measures of similarity and niche overlap. Theoretical Population Biology, 35, 1-21 crossref(new window)

18.
MacArthur, R. H. (1972). Geographical Ecology. Harper and Row, New York

19.
Mann, N. R., Schafer, R. E. and Singpurwalla, N. D. (1974). Methods for Statistical Analysis of Reliability and Life Data. John Wiley & Sons, New York

20.
Matusita, K. (1955). Decision rules, based on the distance for problems of fir, two samples and estimation. The Annals of Mathematical Statistics, 26, 631-640 crossref(new window)

21.
McIntyre, G. A. (1952). A method for unbiased selective samplings using ranked sets. Australian Journal of Agricultural Research, 3, 385-390 crossref(new window)

22.
Mishra, S. N., Shah, A. K. and Lefante, J. J. Jr. (1986). Overlapping coefficient: The generalized t approach. Communications in Statistics-Theory and Methods, 15, 123-128 crossref(new window)

23.
Morisita, M. (1959). Measuring interspecific association and similarity between communities. Memoirs of the Faculty of Kyushu University, Ser. E, Biology, 3, 36-80

24.
Mulekar, M. S. and Mishra, S. N. (1994). Overlap Coefficient of two normal densities: Equal means case. Journal of Japan Statistical Society, 24, 169-180

25.
Mulekar, M. S. and Mishra, S. N. (2000). Confidence interval estimation of overlap: Equal means case. Computational Statistics and Data Analysis, 34, 121-137 crossref(new window)

26.
Mulekar, M. S., Gonzales, S. and Aryal, S. (2001). Estimation and inference for the overlap of two exponential distributions. In Proceedings of American Statistical Association, Joint Statistical Meetings

27.
Muttlak, H. A. (1997). Median ranked set sampling. Journal of Applied Statistical Science, 6, 245-255

28.
Patil, G. P., Sinha, A. K. and Taillie, C. (1999). Ranked set sampling: A bibliography. Environmental Ecological Statistics, 6, 91-98 crossref(new window)

29.
Reiser, B. and Faraggi, D. (1999). Confidence intervals for the overlapping coefficient: The normal equal variance case. The Statistician, 48, 3, 413-418

30.
Samawi, H. M. (2002). On double extreme rank set sample with application to regression estimator. Metron-International Journal of Statistics, LX,1-2

31.
Samawi, H. M. Ahmed, M. S. and Abu Dayyeh, W. (1996a). Estimating the population mean using extreme ranked set sampling. Biometrical Journal, 38, 577-586 crossref(new window)

32.
Samawi, H. M. and Al-Sageer, O. A. M. (2001). On the estimation of the distribution function using extreme and median ranked set sampling. Biometrical Journal, 43, 357-373 crossref(new window)

33.
Samawi, H. M. and Muttlak, H. A. (1996). Estimation of ratio using ranked set sampling. Biometrical Journal, 38, 753-764 crossref(new window)

34.
Samawi, H. M. and Muttlak, H. A. (2001). On ratio estimation using median ranked set sampling. Journal of Applied Statistical Science, 10, 89-98

35.
Samawi H. M., Woodworth G. G and Al-Saleh M. F. (1996b). Two-sample importance resampling for the bootstrap. Metron-International Journal of Statistics, LIV, 3-4

36.
Samawi H. M., Woodworth G. G. and Lemke, J. H. (1998). Power estimation for two- sample tests using importance and antithetic resampling. Biometrical Journal, 40, 341-354 crossref(new window)

37.
Slobodchikoff, C. N. and Schulz, W. C. (1980). Measures of niche overlap. Ecology, 61, 1051-1055 crossref(new window)

38.
Smith, E. P. (1982). Niche breadth, resource availability, and inference. Ecology, 63, 1675-1681 crossref(new window)

39.
Sneath, P. H. A. (1977). A method for testing the distinctness of clusters: a test of the disjunction of two clusters in euclidean space as measured by their overlap. Mathematical Geology, 9, 123-143 crossref(new window)

40.
Weitzman, M. S. (1970). Measures of overlap of income distributions of white and Negro families in the United States. Technical Paper, 22, Departement of Commerce, Bureau of Census, Washington. U.S