1University of Isfahan, Department of Statistics, Isfahan, Iran. PhD. Email: e.zamanzade@sci.ui.ac.ir; ehsanzamanzadeh@yahoo.com
2Hakim Sabzevari University, Department of Statistics, Sabzevar, Iran. PhD. Email: mahdizadeh.m@live.com
This article deals with entropy estimation using ranked set sampling (RSS). Some estimators are developed based on the empirical distribution function and its nonparametric maximum likelihood competitor. The suggested entropy estimators have smaller root mean squared errors than the other entropy estimators in the literature. The proposed estimators are then used to construct goodness of fit tests for inverse Gaussian distribution.
Key words: Judgment ranking, Goodness of fit test, Entropy estimation.
Este artículo trata sobre la estimación de entropía usando muestras de rango ordenado (RSS). Algunos estimadores se desarrollan con base en distribuciones empíricas y si estimación no paramétrica de máxima verosimilitud. Los estimadores de entropía sugeridos tienen menor raíz del error de cuadrados medios que otros reportados en literatura. Los estimadores propuestos son usados para construir pruebas de bondad de ajuste para distribuciones inversas Gaussianas.
Palabras clave: Bondad de ajuste, Estimación de entropía, Ranking de juicios.
Texto completo disponible en PDF
References
]]>1. Chen, H., Stasny, E. A. & Wolfe, D. A. (2005), 'Ranked set sampling for efficient estimation of a population proportion', Statistics in Medicine 24, 3319-3329. [ Links ]
2. Correa, J. C. (1995), 'A new estimator of entropy', Communications in Statistics-Theory Methods 24, 2439-2449. [ Links ]
3. Duembgen, L. & Zamanzade, E. (2013), 'Inference on a distribution function from ranked set samples', arXiv:1304.6950v3. [ Links ]
4. Ebrahimi, N., Habibullah, M. & Soofi, E. (1994), 'Two measures of sample entropy', Statistics & Probability Letters 20, 225-234. [ Links ]
5. Frey, J., Ozturk, O. & Deshpande, J. (2007), 'Nonparametric tests for perfect judgment rankings', Journal of the American Statistical Association 102(48), 708-717. [ Links ]
]]>6. Grzegorzewski, P. & Wieczorkowski, R. (1999), 'Entropy-based goodness-of-fit test for exponentiality', Communications in Statistics-Theory Methods 28, 1183-1202. [ Links ]
7. Haq, A., Brown, J., Moltchanova, E. & Al-Omari, A. (2014), 'Mixed ranked set sampling design', Journal of Applied Statistics 41, 2141-2156. [ Links ]
8. Howard, R. W., Jones, S. C., Mauldin, J. K. & Beal, R. H. (1982), 'Abundance, distribution and colony size estimates for reticulitermes spp. (isopter: rhinotermitidae) in southern mississippi', Environmental Entomology 11, 1290-1293. [ Links ]
9. Huang, J. (1997), 'Asymptotic properties of the npmle of a distribution function based on ranked set samples', The Annals of Statistics 25(3), 1036-1049. [ Links ]
10. Kvam, P. H. (2003), 'Ranked set sampling based on binary water quality data with covariates', Journal of Agricultural, Biological and Environmental Statistics 8, 271-279. [ Links ]
]]>11. Kvam, P. & Samaniego, F. (1994), 'Nonparametric maximum likelihood estimation based on ranked set samples', Journal of the American Statistical Association 89, 526-537. [ Links ]
12. MacEachern, S., Ozturk, O., Wolfe, D. & Stark, G. (2002), 'A new ranked set sample estimator of variance', Journal of the Royal Statistical Society: Series B. 64, 177-188. [ Links ]
13. Mahdizadeh, M. (2012), 'On the use of ranked set samples in entropy based test of fit for the laplace distribution', Revista Colombiana de Estadística 35(3), 443-455. [ Links ]
14. Mahdizadeh, M. & Arghami, N. (2009), 'Efficiency of ranked set sampling in entropy estimation and goodness-of-fit testing for the inverse gaussian law', Journal of Statistical Computation and Simulation 80, 761-774. [ Links ]
15. Mahdizadeh, M. & Zamanzade, E. (2016), 'Kernel-based estimation of P(X Y) in ranked set sampling', Statistics and Operations Research Transactions (SORT) 40(2), 243-266. [ Links ]
]]>16. McIntyre, G. A. (1952), 'A method for unbiased selective sampling using ranked set sampling', Australian Journal of Agricultural Research 3, 385-390. [ Links ]
17. Mudholkar, G. S. & Tian, L. (2002), 'An entropy characterization of the inverse gaussian distribution and related goodness-of-fit test', Journal of Statistical Planning and Inference 102, 211-221. [ Links ]
18. Murray, R. A., Ridout, M. S. & Cross, J. V. (2000), 'The use of ranked set sampling in spray deposit assessment', Aspects of Applied Biology 57, 141-146. [ Links ]
19. Muttlak, H. (1996), 'Pair rank set sampling', Biometrical Journal 38(7), 879-885. [ Links ]
20. Muttlak, H. (1997), 'Median ranked set sampling', Journal of Applied Statistical Sciences, 6, 245-255. [ Links ]
]]>21. Nussbaum, B. D. & Sinha, B. K. (1997), Cost effective gasoline sampling using ranked set sampling, 'Proceedings of the Section on Statistics and the Environment', American Statistical Association, , , p. 83-87. [ Links ]
22. Ozturk, O., Bilgin, O. & Wolfe, D. A. (2005), 'Estimation of population mean and variance in flock management: a ranked set sampling approach in a finite population setting', Journal of Statistical Computation and Simulation 75, 905-919. [ Links ]
23. Perron, F. & Sinha, B. (2004), 'Estimation of variance based on a ranked set sample', Journal of Statistical Planning and Inference 120, 21-28. [ Links ]
24. Samawi, H., Abu-Daayeh, H. & Ahmed, S. (1996), 'Estimating the population mean using extreme ranked set sampling', Biometrical Journal 38, 577-586. [ Links ]
25. Sanhueza, A., Leiva, V. & López-Kleine, L. (2011), 'On the student-t mixture inverse gaussian model with an application to protein production', Revista Colombiana de Estadística 34(1), 177-195. [ Links ]
]]>26. Shannon, C. E. (1948), 'A mathematical theory of communications', Bell System Technical Journal 27, 623-656. [ Links ]
27. Stokes, S. L. (1980), 'Estimation of variance using judgment ordered ranked set samples', Biometrics 36, 35-42. [ Links ]
28. Stokes, S. L. & Sager, T. W. (1988), 'Characterization of a ranked-set sample with application to estimating distribution functions', Journal of the American Statistical Association 83, 374-381. [ Links ]
29. Takahasi, K. & Wakimoto, K. (1968), 'On unbiased estimates of the population mean based on the sample stratified by means of ordering', Annals of the Institute of Statistical Mathematics 20, 1-31. [ Links ]
30. Vasicek, O. (1976), 'A test for normality based on sample entropy', Journal of Royal Statistical Society, Ser B 38, 54-59. [ Links ]
]]>31. Zamanzade, E. & Vock, M. (2015), 'Variance estimation in ranked set sampling using a concomitant variable', Statistics & Probability Letters 105, 1-5. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv40n2a02,
AUTHOR = {Zamanzade, Ehsan and Mahdizadeh, M.},
TITLE = {{Entropy Estimation From Ranked Set Samples With Application to Test of Fit}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2017},
volume = {40},
number = {2}, ]]>
pages = {223-241}
}