Information Measures Based on Sampling Distributions
Information theory and Statistics play an important role in Biological Sciences when we use information measures for the study of diversity and equitability. In this communication, we develop the link among the three disciplines and prove that sampling distributions can be used to develop new information measures. Our study will be an interdisciplinary and will find its applications in Biological systems.
[1] K. McGarigal and B.J. Marks, 1995. FRAGSTATS: Spatial Pattern
Analysis Program for Quantifying Landscape Structure. General
Technical Report (USDA Forestry Service, Corvallis, 1995).
[2] A. Chawla, S. Rajkumar, K.N. Singh, Brij Lal, R.D. Singh and A.K.
Thukral, Plant species diversity along an altitudinal gradient of Bhabha
valley in western Himalaya. Journal of Mountain Science 5 (2008) 157-
177.
[3] A.E. Magurran, Ecological Diversity and its Measurement (Croom
Helm, 1988, London).
[4] M, Gadgil and Meher-Homji, V.M. Ecological diversity. In: J.C. Daniel
and J.S. Serrao (Eds.) Proceedings of the Centenary Seminar of the
Bombay Natural History Society (Oxford University Press, Bombay,
1990).
[5] S.Baumgartner, Measuring Biodiversity (University of Heidelberg,
Heidelberg, 2005).
[6] P.D.S. Kinako, Mathematical elegance and ecological naivety of
diversity indices, African Journal of Ecology 21 (2009) 93-99.
[7] O.Parkash and A.K.Thukral, Statistical measures as measures of
diversity, International Journal of Biomathematics 2009 (In press).
[8] J.H. Havrada and F.Charvat, Quantification methods of classification
process:Concept of structural -entropy, Kybernetika 3, (1967) 30-35.
[9] B. H. Lavenda, Mean Entropies, Open System Infor. Dyn. 12, (2005)
289-302.
[10] A.K. Nanda. and P. Paul, Some results on generalized residual entropy,
Information Sciences 176 (2006) 27-47.
[11] O. Onicescu, Energie Informationelle (C.R.Academic Science, 1966).
[12] O. Parkash, P. K. Sharma and R. Mahajan, New measures of
weighted fuzzy entropy and their applications for the study of
maximum weighted fuzzy entropy principle, Information Sciences 178
(2008) 2389-2395.
[13] O. Parkash, P. K. Sharma and R. Mahajan, Optimization principle for
weighted fuzzy entropy using unequal constraints, Southeast Asian
Bulletin Mathematics 2008 (In Press).
[14] M.C. Rao, V.B.C.,Yunmei and F.Wang, Commulative residual entropy:
a new measure of Information, IEEE Trans. Inform. Theory 50 (2004)
1220-1228.
[15] A. Renyi , On measures of entropy and information, Proc. 4th Ber.
Symp. Math. Stat. and Prob. 1 (1961) 547-561.
[16] C. E. Shannon, A mathematical theory of communication, Bell. Sys.
Tech. Jr. 27(1948) 379-423, 623-659.
[17] E. H. Simpson, Measurement of diversity, Nature 163 (1949) 688.
[18] K. Zyczkowski, Renyi extrapolation of Shannon entropy, Open Syst.
Inf. Dyn., 10 (1948) 297-310.
[1] K. McGarigal and B.J. Marks, 1995. FRAGSTATS: Spatial Pattern
Analysis Program for Quantifying Landscape Structure. General
Technical Report (USDA Forestry Service, Corvallis, 1995).
[2] A. Chawla, S. Rajkumar, K.N. Singh, Brij Lal, R.D. Singh and A.K.
Thukral, Plant species diversity along an altitudinal gradient of Bhabha
valley in western Himalaya. Journal of Mountain Science 5 (2008) 157-
177.
[3] A.E. Magurran, Ecological Diversity and its Measurement (Croom
Helm, 1988, London).
[4] M, Gadgil and Meher-Homji, V.M. Ecological diversity. In: J.C. Daniel
and J.S. Serrao (Eds.) Proceedings of the Centenary Seminar of the
Bombay Natural History Society (Oxford University Press, Bombay,
1990).
[5] S.Baumgartner, Measuring Biodiversity (University of Heidelberg,
Heidelberg, 2005).
[6] P.D.S. Kinako, Mathematical elegance and ecological naivety of
diversity indices, African Journal of Ecology 21 (2009) 93-99.
[7] O.Parkash and A.K.Thukral, Statistical measures as measures of
diversity, International Journal of Biomathematics 2009 (In press).
[8] J.H. Havrada and F.Charvat, Quantification methods of classification
process:Concept of structural -entropy, Kybernetika 3, (1967) 30-35.
[9] B. H. Lavenda, Mean Entropies, Open System Infor. Dyn. 12, (2005)
289-302.
[10] A.K. Nanda. and P. Paul, Some results on generalized residual entropy,
Information Sciences 176 (2006) 27-47.
[11] O. Onicescu, Energie Informationelle (C.R.Academic Science, 1966).
[12] O. Parkash, P. K. Sharma and R. Mahajan, New measures of
weighted fuzzy entropy and their applications for the study of
maximum weighted fuzzy entropy principle, Information Sciences 178
(2008) 2389-2395.
[13] O. Parkash, P. K. Sharma and R. Mahajan, Optimization principle for
weighted fuzzy entropy using unequal constraints, Southeast Asian
Bulletin Mathematics 2008 (In Press).
[14] M.C. Rao, V.B.C.,Yunmei and F.Wang, Commulative residual entropy:
a new measure of Information, IEEE Trans. Inform. Theory 50 (2004)
1220-1228.
[15] A. Renyi , On measures of entropy and information, Proc. 4th Ber.
Symp. Math. Stat. and Prob. 1 (1961) 547-561.
[16] C. E. Shannon, A mathematical theory of communication, Bell. Sys.
Tech. Jr. 27(1948) 379-423, 623-659.
[17] E. H. Simpson, Measurement of diversity, Nature 163 (1949) 688.
[18] K. Zyczkowski, Renyi extrapolation of Shannon entropy, Open Syst.
Inf. Dyn., 10 (1948) 297-310.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52449", author = "Om Parkash and A. K. Thukral and C. P. Gandhi", title = "Information Measures Based on Sampling Distributions", abstract = "Information theory and Statistics play an important role in Biological Sciences when we use information measures for the study of diversity and equitability. In this communication, we develop the link among the three disciplines and prove that sampling distributions can be used to develop new information measures. Our study will be an interdisciplinary and will find its applications in Biological systems.
", keywords = "Entropy, concavity, symmetry, arithmetic mean, diversity, equitability.", volume = "5", number = "3", pages = "293-5", }
