### Distributions of products involving the type II Bessel function random variable

#### Abstract

#### Full Text:

PDF (English)#### References

M. S. ABU-SALIH, (1983), Distribution of the product and the quotient of power-function random variables, “Arab Journal of Mathematics”, 4, pp. 77-90.

R. P. BHARGAVA, C. G. KHATRI, (1981), The distribution of product of independent beta random variables with application to multivariate analysis, “Annals of the Institute of Statistical Mathematics”, 33, pp. 281-287.

A. ERDÉLYI, et al. (eds), (1953), Higher Transcendental Functions, Volume I, McGraw-Hill, New York.

T. S. GLICKMAN, F. XU, (2008), The distribution of the product of two triangular random variables, “Statistics and Probability Letters”, in press.

I. S. GRADSHTEYN, I. M. RHYZIK, (1994), Table of Integrals, Series, and Products, fifth edition, Academic Press, San Diego.

N. L. JOHNSON, S. KOTZ, (1970), Continuous Univariate Distributions , Volume 2, John Wiley and Sons, New York.

H. J. MALIK, R. TRUDEL, (1986), Probability density function of the product and quotient of two correlated exponential random variables, “Canadian Mathematical Bulletin”, 29, pp. 413-418.

A. M. MATHAI, (1993), A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford.

H. PODOLSKI, (1972), The distribution of a product of n independent random variables with generalized gamma distribution, “Demonstratio Mathematica”, 4, pp. 119-123.

A. P. PRUDNIKOV, Y. A. BRYCHOV, O. I. MARICHEV, (1986), Integrals and Series Volumes I and II, Gordon and Breach Science Publishers, Amsterdam.

H. SAKAMOTO, (1943), On the distribution of the product and the quotient of the independent and uniformly distributed random variables, “Tohoku Mathematical Journal”, 49, pp. 243-260.

M. D. SPRINGER, (1979), The Algebra of Random Variables, John Wiley and Sons, New York.

M. D. SPRINGER, W. F. THOMPSON, (1970), The distribution of products of beta, gamma and Gaussian random variables, “SIAM Journal on Applied Mathematics”, 18, pp. 721-737.

H. M. SRIVASTAVA, H. L. MANOCHA, (1984), A Treatise on Generating Functions, John Wiley and Sons, New York.

B. M. STEECE, (1976), On the exact distribution for the product of two beta-distributed random variables, “Metron”, 34, pp. 187-190.

A. STUART, (1962), Gamma-distributed products of independent random variables, “Biometrika”, 49, pp. 564-565.

J. TANG, A. K. GUPTA, (1984), On the distribution of the products of independent beta random variables, “Statistics and Probability Letters”, 2, pp. 165-168.

C. M. WALLGREN, (1980), The distribution of the product of two correlated t variates, “Journal of the American Statistical Association”, 75, pp. 996-1000.

DOI: 10.6092/issn.1973-2201/3582