BibTex RIS Kaynak Göster

RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES

Yıl 2015, Cilt: 8 Sayı: 2, 60 - 73, 01.06.2015

Öz

The Tsallis entropy is a generalization of type α of the Shannon entropy (Tsallis, 1988) that isa non-additive entropy unlike the Shannon entropy and some of other generalized entropy, such as Renyientropy that introduced by Renyi (1961). In this paper, we study the Tsallis entropy based on order statisticsand record values. We show that the parent distributions can be determined uniquely by the equality of Tsallisentropy of order statistics or record values. Also, we characterize symmetric distributions based on Tsallisentropy of order statistics and record values. Finally, we prove that the Tsallis information between orderstatistics and parent random variable, and Tsallis information between record values and parent randomvariable are distribution free. The results are useful in modeling problems and testing statistical hypotheses

Kaynakça

  • Abbasnejad, M. and Arghami, N. R. (2011),Renyi entropy properties of order statistics,Commun. Stat. Theory Methods, 40, 40-52.
  • Abbasnejad, M. and Arghami, N. R. (2011).Renyi entropy properties of records, S. P. I., 141, 2312-2320.
  • Aliprantis, C. D. and Burkinshaw, O. (1981).Principles of Real Analysis. Elsevier North Holland Inc.
  • Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992).A First Course in Order Statistics. New
  • York, John Wiley and Sons. Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998).Records. New York, John Wiley and Sons.
  • Baratpour, S., Ahmadi, J. and Arghami, N. R. (2007). Some characterizations based on entropy of order statistics and record values,Commun. Stat. Theory Methods,36, 47-57.
  • Baratpour, S., Ahmadi, J. and Arghami, N. R. (2008).Characterizations based on Renyi entropy of order statistics and record values,S. P. I., 138, 2544-2551.
  • David, H. A. and Nagaraja, H. N. (2003).Order Statistics. Third ed. John Wiley and Sons, Hoboken, New Jersey.
  • Ebrahimi, N., Habibullah, M. and SooŞ, E. S. (1992).Testing exponentiality based on Kullback-Leibler information, J. R. Stat. Soc., 54, 739-748.
  • Ebrahimi, N., SooŞ, E. S. and Zahedi, H. (2004).Information properties of order statistics and spac- ing,IEEE Trans. Inf. Theory, 50, 177-183.
  • Fashandi, M. and Ahmadi, J. (2012). Characterizations of symmatric distributions based on Revyi entropy,Stat. Probab. Lett., 82, 798-804.
  • Goffman, C. and Pedrick, G. (1965).First Course in Functional Analysis. Prentice-Hall, Inc.
  • Gupta, R. C., Taneja, H. C. and Thapliyal, R. (2014). Stochastic comparisons based on residual entropy of order statistics and some characterization results,Stat. Theory Appl. (JSTA), 13 (1), 27-37.
  • Habibi, A., Yousefzadeh, F., Amini, M. and Arghmi, N. R. (2007). Testing exponentiality based on record values,Iranian Statist. Soc. (JIRSS), 6, 77-87.
  • Hamity, V. H. and Barraco, D. E. (1996).Generalized nonextensive thermodynamics applied to the cosmical background radiation in Robertson-Walker universe,Phys. Rev. Lett., 76, 4664-4666.
  • Havrda, J. and Charvat, F. (1967).QuantiŞcation method of classiŞcation process: Concept of structural α-entropy,Kybernetika, 3, 30-35.
  • Higgins, J. R.(2004).Completeness and Basis Properties of Sets of Special Functions. Cambridge Uni- versity Press, New York.
  • Hwang, J. S. and Lin, G. D. (1984). On a generalized moment problem II, A. M. S., 91, 577-580.
  • Kamps, U. (1994).Reliability properties of record values from non-identically distributed random vari- ables,Commun. Stat. Theory Methods, 23, 2101-2112.
  • Kullback, S. and Leibler, R. A.(1951). On information and sufficiency, Ann. Math. Stat., 22, 79-86.
  • Kumar, V. and Taneja, H. C. (2011).A generalized entropy-based residual lifetime distribu- tions,Biomathematics, 4, 171-184.
  • Nanda, A. K. and Paul, P. (2006).Some results on generalized residual entropy, Inf. Sci., 176, 27-47.
  • Park, S. (2005).Testing exponentiality based on Kullback-Leibler information with the Type II censored data,IEEE Trans. Reliab., 54, 22-26.
  • Renyi, A. (1961).On measures of entropy and information. Proc. Fourth. Berkeley Symp. Math. Stat.
  • Prob., University of California Press, Berkeley, pp. 547-561. Raqab, M. Z. and Awad, A. M.(2000).Characterizations of the Pareto and related distributions, Metrika, , 63-67.
  • Raqab, M. Z. and Awad, A. M.(2001).A note on characterization based on Shannon entropy of record statistics,Statistics, 35, 411-413.
  • Shaked, M. and Shanthikumar, J. G.(1994).Stochastic Orders and Their Applications. New York, Aca- demic Press.
  • Shannon, C. E.(1948). A mathematical theory of communication,Bell Syst. Tech. J., 27, 379-432.
  • Thapliyal, R. and Taneja, H. C. (2013).Order Statistics Based Measure Of Past Entropy, Interdisci- plinary Sciences,1, 63-70.
  • Thapliyal, R., Taneja, H. C. and Kumar, V. (2015).Characterization results based on non-additive entropy of order statistics,Physica A:Statistical Mechanics and Its Applications, 417, 297-303.
  • Tong, S., Bezerianos, A., Paul, J., Zhu, Y. and Thakor, N. (2002).Nonextensive entropy measure of EEG following brain injury from cardiac arrest, Physica A: Statistical Mechanics and its Applications, 305, 628.
  • Tsallis, C. (1988).Possible generalization of Boltzmann-Gibbs Statistics, J. Stat. Phys., 52, 479-487.
  • Tsallis, C. (1998).Generalized entropy-based criterion for consistent testing,Phys. Rev. E, 58, 1442-1445.
  • Tsallis, C. (2009).Introduction to nonextensive statistical mechanics: approaching a complex world. New York, Springer.
  • Tsallis, C.(2014).Non-additive entropies Foundations and applications in Physics and elsewhere. http://www.american.edu/cas/economics/info-metrics/upload/Constantino-Tsallis1.pdf
  • Vasicek, O. (1976).A test for normality based on sample entropy, J. R. Stat. Soc. , 38, 54-59.
  • Wilk, G. and Woldarczyk, Z. (2008).Example of a possible interpretation of Tsallis entropy,Physica A:
  • Statistical Mechanics and Its Applications, 341, 4809-4813.
  • Yu, M., Zhanfang, C. and Hongbiao, Z. (2009).Research of automatic medical image segmentation algorithm based on Tsallis entropy and improved PCNN.,IEEE proceddings on ICMA, 1004-1008.
  • Zhang, Z. (2007).Uniform Estimates on the Tsallis Entropies, L. M. P., 80, 171-181.
Yıl 2015, Cilt: 8 Sayı: 2, 60 - 73, 01.06.2015

Öz

Kaynakça

  • Abbasnejad, M. and Arghami, N. R. (2011),Renyi entropy properties of order statistics,Commun. Stat. Theory Methods, 40, 40-52.
  • Abbasnejad, M. and Arghami, N. R. (2011).Renyi entropy properties of records, S. P. I., 141, 2312-2320.
  • Aliprantis, C. D. and Burkinshaw, O. (1981).Principles of Real Analysis. Elsevier North Holland Inc.
  • Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992).A First Course in Order Statistics. New
  • York, John Wiley and Sons. Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998).Records. New York, John Wiley and Sons.
  • Baratpour, S., Ahmadi, J. and Arghami, N. R. (2007). Some characterizations based on entropy of order statistics and record values,Commun. Stat. Theory Methods,36, 47-57.
  • Baratpour, S., Ahmadi, J. and Arghami, N. R. (2008).Characterizations based on Renyi entropy of order statistics and record values,S. P. I., 138, 2544-2551.
  • David, H. A. and Nagaraja, H. N. (2003).Order Statistics. Third ed. John Wiley and Sons, Hoboken, New Jersey.
  • Ebrahimi, N., Habibullah, M. and SooŞ, E. S. (1992).Testing exponentiality based on Kullback-Leibler information, J. R. Stat. Soc., 54, 739-748.
  • Ebrahimi, N., SooŞ, E. S. and Zahedi, H. (2004).Information properties of order statistics and spac- ing,IEEE Trans. Inf. Theory, 50, 177-183.
  • Fashandi, M. and Ahmadi, J. (2012). Characterizations of symmatric distributions based on Revyi entropy,Stat. Probab. Lett., 82, 798-804.
  • Goffman, C. and Pedrick, G. (1965).First Course in Functional Analysis. Prentice-Hall, Inc.
  • Gupta, R. C., Taneja, H. C. and Thapliyal, R. (2014). Stochastic comparisons based on residual entropy of order statistics and some characterization results,Stat. Theory Appl. (JSTA), 13 (1), 27-37.
  • Habibi, A., Yousefzadeh, F., Amini, M. and Arghmi, N. R. (2007). Testing exponentiality based on record values,Iranian Statist. Soc. (JIRSS), 6, 77-87.
  • Hamity, V. H. and Barraco, D. E. (1996).Generalized nonextensive thermodynamics applied to the cosmical background radiation in Robertson-Walker universe,Phys. Rev. Lett., 76, 4664-4666.
  • Havrda, J. and Charvat, F. (1967).QuantiŞcation method of classiŞcation process: Concept of structural α-entropy,Kybernetika, 3, 30-35.
  • Higgins, J. R.(2004).Completeness and Basis Properties of Sets of Special Functions. Cambridge Uni- versity Press, New York.
  • Hwang, J. S. and Lin, G. D. (1984). On a generalized moment problem II, A. M. S., 91, 577-580.
  • Kamps, U. (1994).Reliability properties of record values from non-identically distributed random vari- ables,Commun. Stat. Theory Methods, 23, 2101-2112.
  • Kullback, S. and Leibler, R. A.(1951). On information and sufficiency, Ann. Math. Stat., 22, 79-86.
  • Kumar, V. and Taneja, H. C. (2011).A generalized entropy-based residual lifetime distribu- tions,Biomathematics, 4, 171-184.
  • Nanda, A. K. and Paul, P. (2006).Some results on generalized residual entropy, Inf. Sci., 176, 27-47.
  • Park, S. (2005).Testing exponentiality based on Kullback-Leibler information with the Type II censored data,IEEE Trans. Reliab., 54, 22-26.
  • Renyi, A. (1961).On measures of entropy and information. Proc. Fourth. Berkeley Symp. Math. Stat.
  • Prob., University of California Press, Berkeley, pp. 547-561. Raqab, M. Z. and Awad, A. M.(2000).Characterizations of the Pareto and related distributions, Metrika, , 63-67.
  • Raqab, M. Z. and Awad, A. M.(2001).A note on characterization based on Shannon entropy of record statistics,Statistics, 35, 411-413.
  • Shaked, M. and Shanthikumar, J. G.(1994).Stochastic Orders and Their Applications. New York, Aca- demic Press.
  • Shannon, C. E.(1948). A mathematical theory of communication,Bell Syst. Tech. J., 27, 379-432.
  • Thapliyal, R. and Taneja, H. C. (2013).Order Statistics Based Measure Of Past Entropy, Interdisci- plinary Sciences,1, 63-70.
  • Thapliyal, R., Taneja, H. C. and Kumar, V. (2015).Characterization results based on non-additive entropy of order statistics,Physica A:Statistical Mechanics and Its Applications, 417, 297-303.
  • Tong, S., Bezerianos, A., Paul, J., Zhu, Y. and Thakor, N. (2002).Nonextensive entropy measure of EEG following brain injury from cardiac arrest, Physica A: Statistical Mechanics and its Applications, 305, 628.
  • Tsallis, C. (1988).Possible generalization of Boltzmann-Gibbs Statistics, J. Stat. Phys., 52, 479-487.
  • Tsallis, C. (1998).Generalized entropy-based criterion for consistent testing,Phys. Rev. E, 58, 1442-1445.
  • Tsallis, C. (2009).Introduction to nonextensive statistical mechanics: approaching a complex world. New York, Springer.
  • Tsallis, C.(2014).Non-additive entropies Foundations and applications in Physics and elsewhere. http://www.american.edu/cas/economics/info-metrics/upload/Constantino-Tsallis1.pdf
  • Vasicek, O. (1976).A test for normality based on sample entropy, J. R. Stat. Soc. , 38, 54-59.
  • Wilk, G. and Woldarczyk, Z. (2008).Example of a possible interpretation of Tsallis entropy,Physica A:
  • Statistical Mechanics and Its Applications, 341, 4809-4813.
  • Yu, M., Zhanfang, C. and Hongbiao, Z. (2009).Research of automatic medical image segmentation algorithm based on Tsallis entropy and improved PCNN.,IEEE proceddings on ICMA, 1004-1008.
  • Zhang, Z. (2007).Uniform Estimates on the Tsallis Entropies, L. M. P., 80, 171-181.
Toplam 40 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA52PE63PP
Bölüm Araştırma Makalesi
Yazarlar

S. Baratpour Bu kişi benim

A. H. Khammar. Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 8 Sayı: 2

Kaynak Göster

APA Baratpour, S., & Khammar., A. H. (2015). RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES. Istatistik Journal of The Turkish Statistical Association, 8(2), 60-73.
AMA Baratpour S, Khammar. AH. RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES. IJTSA. Haziran 2015;8(2):60-73.
Chicago Baratpour, S., ve A. H. Khammar. “RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES”. Istatistik Journal of The Turkish Statistical Association 8, sy. 2 (Haziran 2015): 60-73.
EndNote Baratpour S, Khammar. AH (01 Haziran 2015) RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES. Istatistik Journal of The Turkish Statistical Association 8 2 60–73.
IEEE S. Baratpour ve A. H. Khammar., “RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES”, IJTSA, c. 8, sy. 2, ss. 60–73, 2015.
ISNAD Baratpour, S. - Khammar., A. H. “RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES”. Istatistik Journal of The Turkish Statistical Association 8/2 (Haziran 2015), 60-73.
JAMA Baratpour S, Khammar. AH. RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES. IJTSA. 2015;8:60–73.
MLA Baratpour, S. ve A. H. Khammar. “RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES”. Istatistik Journal of The Turkish Statistical Association, c. 8, sy. 2, 2015, ss. 60-73.
Vancouver Baratpour S, Khammar. AH. RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES. IJTSA. 2015;8(2):60-73.