A modified Bessel distribution of the second kind

Authors

  • Saralees Nadarajah University of Manchester

DOI:

https://doi.org/10.6092/issn.1973-2201/3518

Abstract

Motivated by a Bayesian inference problem, a modification of the Bessel function distribution is introduced. Various particular cases, expressions for its moments and estimation procedures are derived. An application is illustrated to failure data.

References

V. V. ANH, R. MCVINISH, C. PESEE, (2005), Estimation and simulation of the Riesz-Bessel distribution, “Communications in Statistics-Theory and Methods”, 34, pp. 1881-1897.

R. CHHIKARA, L. FOLKS, (1989), The Inverse Gaussian distribution: theory, methodology, and applications, Marcel Dekker, New York.

A.K. GUPTA, S. NADARAJAH, (2006), Beta Bessel distributions, “International Journal of Mathematics and Mathematical Sciences”, Article ID 16156.

B. HARRIS, A.P. SOMS, (1974), Properties of the generalized incomplete modified Bessel distributions with applications to reliability theory, “Journal of the American Statistical Association”, 69, pp. 259-263.

P. KIELCZYNSKI, W. PAJEWSKI, (1993), Acoustic field of gaussian and Bessel transducers, “Journal of the Acoustical Society of America”, 94, pp. 1719-1721.

P. KIELCZYNSKI, W. PAJEWSKI, M. SZALEWSKI, (1993), Ultrasonic transducers with Bessel–function distribution of vibrational amplitude on their surfaces, “IEEE Transactions on Robotics and Automation”, 9, pp. 732-739.

J. LIEBLEIN, M. ZELEN, (1956), Statistical investigation of the fatigue life of deep-groove ball bearings, “Journal Research of the National Bureau of Standards”, 57, pp. 273-316.

F. MCNOLTY, (1967), Applications of Bessel function distributions, “Sankhyā”, B, 29, pp. 235-248.

A.P. PRUDNIKOV, Y.A. BRYCHKOV, O.I. MARICHEV, (1986), Integrals and series, volumes 1, 2 and 3, Gordon and Breach Science Publishers, Amsterdam.

N.A. SALINGAROS, (1991), Optimal current distribution for energy-storage in superconducting magnets, “Journal of Applied Physics”, 69, pp. 531-533.

V. SESHADRI, (1986), The Inverse Gaussian distribution: statistical theory and applications, Springer Verlag, New York.

H.M. SRIVASTAVA, S. NADARAJAH, (2006), Some families of Bessel distributions and their applications, “Integral Transforms and Special Functions”, 17, pp. 65-73.

L. THABANE, B.M.G. KIBRIA, (1999), On the generalized modified power Bessel distribution. “Journal of Statistical Research”, 33, pp. 9-22.

Downloads

Published

2007-12-31

How to Cite

Nadarajah, S. (2007). A modified Bessel distribution of the second kind. Statistica, 67(4), 405–413. https://doi.org/10.6092/issn.1973-2201/3518

Issue

Section

Articles