Abstract
A claim is made in the paper Nadarajah and Kotz [On the q-type distributions, Physica A 377:465–468, (2007)] that the many q-densities, which are widely used in physics literature, are special cases of or associated with Burr distributions in classical statistical literature. In the present paper it is pointed out that the q-densities are not coming from Burr distributions or from other classical statistical distributions, and that q-distributions are extensions of the limiting forms for q → 1. It is also shown that a statistical distribution which contains all q-distributions as special cases is the pathway model of Mathai [A pathway to matrix-variate gamma and normal densities, Linear Algebra and Its Applications 396:317–328, (2005)]. Tsallis statistics and superstatistics of Beck and Cohen [Superstatistics, Physica A 322:267–275, (2003)] are also examined here in the light of the discussions.
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References
Nadarajah, S., Kotz, S.: On the q-type distributions. Physica A 377, 465–468 (2007).
Beck, C., Cohen, E.G.D.: Superstatistics. Physica A 322, 267–275 (2003).
Beck, C.: Stretched exponentials from superstatistics. Physica A 365, 96–101 (2006).
Mathai, A.M., Haubold, H.J.: Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy. Physica A 375, 110–122 (2007).
Tsallis, C.: Possible generalizations of Boltzmann-Gibbs statistics. Journal of Statistical Physics 52, 479–487 (1988).
Mathai, A.M.: A pathway to matrix-variate gamma and normal densities. Linear Algebra and Its Applications 396, 317–328 (2005).
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Nair, S.S., Kattuveettil, A. (2010). Some Remarks on the Paper “On the q-type Distributions”. In: Haubold, H., Mathai, A. (eds) Proceedings of the Third UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science. Astrophysics and Space Science Proceedings. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03325-4_2
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DOI: https://doi.org/10.1007/978-3-642-03325-4_2
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