86
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Mixture Models and the Krätzel Integral Transform

Pages 390-405 | Received 08 Sep 2012, Accepted 29 Oct 2012, Published online: 15 Dec 2014

References

  • Baricz, A., Jankov, D., Pogány, T.K. (2012). Turan type inequalities for Krätzel functions. J. Math. Anal. Appl 388:716–724.
  • Bithas, P. (2009). Weibull-Gamma composite distribution: An alternative multipath/shadowing fading model. Electronic Letters 45:749–751.
  • Böhning, D. (1999). Computer-assisted Analysis of Mixtures. New York: Marcel Dekker Inc.
  • Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G. (1953). Higher Transcendental Functions, Vol. I. New York: McGraw-Hill, (Reprinted: Krieger, Melbourne, Florida, 1981).
  • Everitt, B.S., Hand, D.J. (1981). Finite Mixtures Distributions. London: Chapman and Hall.
  • Gupta, S., Huang, W.T. (1981). On mixtures of distributions: A survey and some new results on ranking and selection. Sankhya B 43:245–290.
  • Jakeman, E., Puesy, P.N. (1976). A model for non-rayleigh sea echo. IEEE Trans. Antennas Propagation 24:806–814.
  • Krätzel, E. (1979). Integral Transformations of Bessel type in Generalized Functions and Operational Calculus. In: Proceedings of International Conference on Varna 1975 (pp. 148–155). Sofia: Bulgarian Academy of Sciences.
  • Lindsay, B., Roeder, K. (1993). Uniqueness of estimation and identifiability in mixture models. Can. J. Stat. 21:139–147.
  • Mathai, A.M., Saxena, R.K., Haubold, H.J. (2010). The H-function: Theory and Applications. New York: Springer.
  • Mathai, A.M. (2012). Generalized Krätzel integral and associated statistical densities. Int. J. Math. Anal. 6:2501–2510.
  • Malik, H., (1986). Probability density function of the product and quotient of two correlated exponential random variables. Can. Math. Bull. 29:413–418.
  • McLachlan, J.A., Peel, D. (2000). Finite Mixture Models. New York: John Wiley and Sons.
  • McLachlan, G., Basford, K. (1988). Mixture Models: Inference and Application to Clustering. New York: Marcel Dekker Inc.
  • Redner, R., Walker, H. (1984). Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26:195–230.
  • Salo, J., El-Sallabi, H.M., Vainikainen, P. (2006). The distribution of the product of independent Rayleigh random variables. IEEE Trans. Antennas Propag. 54:639–643.
  • Shankar, P.M., Dumane, V.A., Reid, J.M., Genis, V., Forsberg, F., Piccoli, C.W., Goldberg, B.B. (2000). Use of the K-distribution for classification of breast masses. Ultrasound Med. Biol. 26:1503–1510.
  • Titterington, D.M., Smith, A. F.M., Markov, U.E. (1985). Statistical Analysis of Finite Mixture Distributions. New York: John Wiley and Sons.
  • Titterington, D.M. (1990). Some recent research in the analysis of mixture distributions. Stat. 21:619–941.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.