Abstract
The Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of masses of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented. Finally, a possible physical mechanism that produces Pareto tails for the distribution of the masses of stars is presented.
[1] V. Pareto, Cours d’ economie politique (Rouge, Lausanne, 1896) Search in Google Scholar
[2] M. Evans, N. Hastings, P. Peacock, Statistical Distributions, 3rd edition (John Wiley & Sons Inc, New York, 2000) Search in Google Scholar
[3] A. Cohen, B. Whitten, Parameter Estimation in reliability and Life Span Models (Marcel Dekker, New York, 1988) Search in Google Scholar
[4] D. Devoto, S. Martnez, Math. Geol. 30, 661 (1998) http://dx.doi.org/10.1023/A:102239121823310.1023/A:1022391218233Search in Google Scholar
[5] I. Aban, M. Meerschaert, A. Panorska, J. Am. Stat. Assoc. 101, 270 (2006) http://dx.doi.org/10.1198/01621450500000041110.1198/016214505000000411Search in Google Scholar
[6] K. Rehfeldt, J.M. Boggs, L.W. Gelhar, Water Resour. Res. 28, 3309 (1992) http://dx.doi.org/10.1029/92WR0175810.1029/92WR01758Search in Google Scholar
[7] E.E. Salpeter, Astrophys. J. 121, 161 (1955) http://dx.doi.org/10.1086/14597110.1086/145971Search in Google Scholar
[8] P. Kroupa, Monthly Notices of the RAS 322, 231 (2001) http://dx.doi.org/10.1046/j.1365-8711.2001.04022.x10.1046/j.1365-8711.2001.04022.xSearch in Google Scholar
[9] K.R. Lang, Astrophysical formulae (Springer, New York, 1999) 10.1007/978-3-662-21639-2Search in Google Scholar
[10] R. Schlickeiser, Cosmic ray astrophysics (Springer, Berlin, 2002) 10.1007/978-3-662-04814-6Search in Google Scholar
[11] E.M. Rossi, Nuovo Cimento C 28, 387 (2005) Search in Google Scholar
[12] J.S. Bloom, D.A. Frail, R. Sari, Astron. J. 121, 2879 (2001) http://dx.doi.org/10.1086/32109310.1086/321093Search in Google Scholar
[13] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables (Dover, New York, 1965) 10.1063/1.3047921Search in Google Scholar
[14] D. von Seggern, CRC Standard Curves and Surfaces (CRC, New York, 1992) Search in Google Scholar
[15] W.J. Thompson, Atlas for computing mathematical functions (Wiley-Interscience, New York, 1997) Search in Google Scholar
[16] I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic Press, San Diego, 2000) Search in Google Scholar
[17] A. Prudnikov, O. Brychkov, Y. Marichev, Integrals and Series (Gordon and Breach Science Publishers, Amsterdam, 1986) Search in Google Scholar
[18] M. Masoom Ali, S. Nadarajah, Comput. Commun. 30, 1 (2006) http://dx.doi.org/10.1016/j.comcom.2006.07.00310.1016/j.comcom.2006.07.003Search in Google Scholar
[19] L. Zaninetti, Astronomische Nachrichten 326, 754 (2005) http://dx.doi.org/10.1002/asna.20051040810.1002/asna.200510408Search in Google Scholar
[20] L. Zaninetti, A. Cellino, V. Zappala, Astronom. Astrophys. 294, 270 (1995) Search in Google Scholar
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