Skip to main content
SpringerLink
Log in

The Inverse MaxEnt and MinxEnt Principles and their Applications

  • Chapter
Maximum Entropy and Bayesian Methods

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 39))

Abstract

Two inverse MaxEnt (maximum entropy) and two inverse MinxEnt (minimum cross-entropy) principles are stated followed by some applications taken from diverse fields. A case is made out for the use of generalized measures of entropy and cross-entropy which naturally arise in such inverse principles.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aczel, J. and Daroczy, Z. (1975) On Measures of Information and their Characterization, Academic Press, New York.

    Google Scholar 

  2. Aczel, J., Forte, B., and Ng, C.T. (1974) ‘Why Shannon and Hartley Entropies are Natural?’, Adv. Appl. Prob., Vol. 6, 131–146.

    Article  MathSciNet  MATH  Google Scholar 

  3. Aczel, J. and Forte, B. (1985) ‘Generalized Entropies and MaxEnt Principle’, in J.H. Justice (ed.), Maximum Entropy and Bayesian Methods in Applied Statistics, Cambridge University Press, pp. 95–100.

    Google Scholar 

  4. Bass, F.M. (1969) ‘A New Product Growth Model for Consumer Durables’, Management Science, Vol. , 215–227.

    Google Scholar 

  5. Bass, F.M. (1974) ‘Theory of stochastic preference and brand switching’, J. Market. Res., Vol. 11, 1–20.

    Article  MathSciNet  Google Scholar 

  6. Behara, M. and Chawla, J.S. (1974) ‘Generalised Gamma Entropy’, Selecta Statistica Canadiana, Vol. 2, 15–39.

    MathSciNet  Google Scholar 

  7. Bhattacharya, A. (1943) ‘On a measure of Divergence between two Statistical Populations defined by their Probability Distributions’, Bull. Cal. Math. Soc., Vol. 35, 99–109.

    Google Scholar 

  8. Burg, J.P. (1972) ‘The Relationship between Maximum Entropy Spectra and Maximum Likelihood Spectra’, in D.G. Childers (ed.), Modern Spectral Analysis, IEEE Press, USA, pp. 130–131.

    Google Scholar 

  9. Csiszer, I. (1972) ‘A Class of Measures of Informativity of Observation Channels’, Periodic. Math. Hungarica, Vol. 2, 191–213.

    Article  Google Scholar 

  10. Ferreri, C. (1980) ‘Hypoentropy and Related Heterogeneity Divergence and Information Measures’, Statistica (Bologna), Vol. 40, No. 2, 155–168.

    MathSciNet  MATH  Google Scholar 

  11. Fisher, J.C. and Pry, R.H. (1971) ‘A Simple Substitution Model for Technological Change’, Technological Forecasting and Social Change, Vol. 2, 75–88.

    Article  Google Scholar 

  12. Floyd, A. (1968) ‘A Methodology for Trend Forecasting of Figures of Merit.’, in J. Bright (ed.), Technological Forecasting for Industry and Government: Methods and Applications, Prentice-Hall Inc., Englewood Cliffs, N.J., USA, pp. 95–109.

    Google Scholar 

  13. Gompertz, B. (1825), Phil. Trans. Roy. Soc., Vol. 115, 513.

    Article  Google Scholar 

  14. Havrda, J.H. and Charvat, F. (1967) ‘Quantification Methods of Classification Processes Concepts of Structural & Entropy’, Kybernetica, Vol. 3, 30–35.

    MathSciNet  MATH  Google Scholar 

  15. Herniter, J.D. (1973) ‘An Entropy Model of Brand Purchase Behaviour’, J. Market. Res., Vol. 10, 361–373.

    Article  Google Scholar 

  16. Jaynes, E.T. (1957) ‘Information Theory and Statistical Mechanics’, Physical Reviews, Vol. 106, 620–630.

    Article  MathSciNet  Google Scholar 

  17. Kapur, J.N. (1967) ‘Generalised entropies of order a and type ß’, The Maths. Seminar, Vol. 4, 78–94.

    MathSciNet  Google Scholar 

  18. Kapur, J.N. (1972) ‘Measures of uncertainty, mathematical programming and physics’, J. Ind. Soc. Agri. Stat., Vol. 24, 47–66.

    Google Scholar 

  19. Kapur, J.N. (1983) ‘Derivation of logistic law of population growth from maximum entropy principle’, Nat. Acad. Sci. Letters, Vol. 6, No. 12, 429–433.

    MathSciNet  MATH  Google Scholar 

  20. Kapur, J.N. (1983) ‘Comparative assessment of various measures of entropy’, J. Inf. and Opt. Sci., Vol. 4, No. 1, 207–232.

    MathSciNet  MATH  Google Scholar 

  21. Kapur, J.N. (1984) ‘A Comparative assessment of various measures of directed divergence’, Advances in Management Studies, Vol. 3, 1–16.

    Google Scholar 

  22. Kapur, J.N. (1986) ‘Four families of Measures of Entropy’, Ind. J. Pure and App. Maths., Vol. 17, No. 4, 429–449.

    MathSciNet  MATH  Google Scholar 

  23. Kapur, J.N. (1988) Maximum-Entropy Models in Science and Engineering, Wiley Eastern Publishers, New Delhi, India.

    Google Scholar 

  24. Kapur, J.N. (1985) Mathematical Models in Biology and Medicine, Affiliated East West Publishers, New Delhi, India.

    MATH  Google Scholar 

  25. Kapur, J.N. and Kumar, V. (1985) ‘A new derivation of pro duct-form probability distributions for queuing theory networks’, Ind. J. Management and Systems, Vol. 1, No. 3, 109–118.

    Google Scholar 

  26. Kapur, J.N. and Kesavan, H.K. (1987) The Generalised Maximum Entropy Principle, Sandford Educational Press, Waterloo, Canada.

    Google Scholar 

  27. Kapur, J.N. and Kesavan, H.K. (1988) ‘A new approach to the study of probabilistic systems’, Int. J. Management Systems, Vol. 4, No. 1, 67–70.

    Google Scholar 

  28. Kapur, J.N. and Kesavan, H.K. (1989) ‘Maximum Entropy Models’, Proc. Symp. Math. Modelling, IIT, Madras, World Scientific Publishers, Singapore.

    MATH  Google Scholar 

  29. Kesavan, H.K. and Kapur, J.N. (1989) ‘Generalised Maximum Entropy Principle’, IEEE Trans. Systems, Man and Cybernetics, (to appear).

    Google Scholar 

  30. Kesavan, H.K. and Kapur, J.N. (1989) ‘On the families of solution of generalised maximum entropy and minimum cross-entropy principle’, Int. J. Gen. Syst., (to appear).

    Google Scholar 

  31. Kesavan, H.K. and Kapur, J.N. (1989) ‘Maximum Entropy And Minimum Cross-Entropy Principles: Need for a Broader Perspective’ in P. Fougere (ed.), Maximum Entropy and Bayesian Methods, Dartmouth College, Kluwer Academic Publishers, Dordecht, (to appear).

    Google Scholar 

  32. Kullback, S. (1959) Information Theory and Statistics, John Wiley, New York, USA.

    MATH  Google Scholar 

  33. Kullback, S. and Leibler, R.A. (1951) ‘On Information and Sufficiency’, Ann. Math. Stat., Vol. 22, 79–86.

    Article  MathSciNet  MATH  Google Scholar 

  34. Purcaro, C. (1973) ‘A new magnitude frequency relation for earthquakes and a classification of relation types’, Geophy. J. Roy. Ast. Soc., Vol. 42, 61–79.

    Google Scholar 

  35. Rao, C.R. (1973) Linear Statistical Inference and its Applications, Wiley Eastern, New Delhi, India.

    Book  MATH  Google Scholar 

  36. Renyi, A., (1961) On Measures Of Entropy and Informaton, Proc. 4th Berkeley Symposium Maths. Stat. Prob., vol 1, pp. 547–561.

    MathSciNet  Google Scholar 

  37. Shannon, C, E. (1948) ‘A Mathematical Theory of Communication’, Bell System Tech. J., Vol. 27, pp. 379–423, and 623–659.

    MathSciNet  MATH  Google Scholar 

  38. Sharif, M.N. and Kabir, G.A. (1976) ‘A generalised model for forecasting technological substitution’, Technological Forecasting and Social Change, Vol. 8, 353–364.

    Article  Google Scholar 

  39. Sharma, B.D. and Taneja, I.J. (1974) ‘Entropy of type (α, β) and other generalised measures of information’, Matrica, Vol. 22, 205–214.

    MathSciNet  Google Scholar 

  40. Sharma, B.D. and Mittal, D.P. (1975) ‘New non-additive measures of entropy for discrete probability distributions’, J. Math. Sci., Vol. 10, 28–40.

    MathSciNet  Google Scholar 

  41. Theil, H. (1967) Economics and Information Theory, North Holland Publishers, Amsterdam.

    Google Scholar 

  42. Troibus, M. (1966) Rational Descriptions, Decisions and Designs, Pergamon Press, Oxford.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Waterloo, Canada

    J. N. Kapur (Adjunct Professor) & H. K. Kesavan (Professor)

Authors
  1. J. N. Kapur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. K. Kesavan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Paul F. Fougère

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Kluwer Academic Publishers

About this chapter

Cite this chapter

Kapur, J.N., Kesavan, H.K. (1990). The Inverse MaxEnt and MinxEnt Principles and their Applications. In: Fougère, P.F. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0683-9_30

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-0683-9_30

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6792-8

  • Online ISBN: 978-94-009-0683-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation