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SOME ALGEBRA FOR PEARSON TYPE VII RANDOM VARIABLES
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 Title & Authors
SOME ALGEBRA FOR PEARSON TYPE VII RANDOM VARIABLES
Nadarajah, Saralees;
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 Abstract
The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Pearson type VII random variables.
 Keywords
Pearson type VII distribution;product of random variables;ratio of random variables;
 Language
English
 Cited by
1.
An alpha-power extension for the Birnbaum–Saunders distribution, Statistics, 2014, 48, 4, 896  crossref(new windwow)
 References
1.
M. S. Abu-Salih, Distributions of the product and the quotient of power-function random variables, Arab J. Math. 4 (1983), no. 1-2, 77-90

2.
A. P. Basu and R. H. Lochner, On the distribution of the ratio of two random variables having generalized life distributions, Technometrics 13 (1971), 281-287 crossref(new window)

3.
R. P. Bhargava and C. G. Khatri, The distribution of product of independent beta random variables with application to multivariate analysis, Ann. Inst. Statist. Math. 33 (1981), no. 2, 287-296 crossref(new window)

4.
M. S. Feldstein, The error of forecast in econometric models when the forecast-period exogenous variables are stochastic, Econometrica 39 (1971), no. 1, 55-60 crossref(new window)

5.
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Translated from the Russian. Sixth edition. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. Academic Press, Inc., San Diego, CA, 2000

6.
H. G. Grubel, Internationally diversified portfolios : welfare gains capital flows, The American Economic Review 58 (1968), no. 5, 1299-1314

7.
H. L. Harter, On the distribution of Wald's classification statistic, Ann. Math. Statistics 22 (1951), 58-67 crossref(new window)

8.
D. L. Hawkins and C.-P. Han, Bivariate distributions of some ratios of independent noncentral chi-square random variables, Comm. Statist. A-Theory Methods 15 (1986), no. 1, 261-277 crossref(new window)

9.
P. J. Korhonen and S. C. Narula, The probability distribution of the ratio of the absolute values of two normal variables, J. Statist. Comput. Simulation 33 (1989), no. 3, 173-182 crossref(new window)

10.
S. Kotz, T. J. Kozubowski, and K. Podgorski, The Laplace Distribution and Generalizations, A revisit with applications to communications, economics, engineering, and finance. Birkhauser Boston, Inc., Boston, MA, 2001

11.
H. J. Malik and R. Trudel, Probability density function of the product and quotient of two correlated exponential random variables, Canad. Math. Bull. 29 (1986), no. 4, 413-418 crossref(new window)

12.
G. Marsaglia, Ratios of normal variables and ratios of sums of uniform variables, J. Amer. Statist. Assoc. 60 (1965), 193-204 crossref(new window)

13.
S. Nadarajah and S. Kotz, Skewed distributions generated by the normal kernel, Statist. Probab. Lett. 65 (2003), no. 3, 269-277 crossref(new window)

14.
T. Pham-Gia, Distributions of the ratios of independent beta variables and applications, Comm. Statist. Theory Methods 29 (2000), no. 12, 2693-2715 crossref(new window)

15.
H. Podolski, The distribution of a product of n independent random variables with generalized gamma distribution, Demonstratio Math. 4 (1972), 119-123

16.
S. J. Press, The t-ratio distribution, J. Amer. Statist. Assoc. 64 (1969), 242-252 crossref(new window)

17.
S. B. Provost, On the distribution of the ratio of powers of sums of gamma random variables, Pakistan J. Statist. 5 (1989), no. 2, 157-174

18.
A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, volumes 1, 2 and 3, Gordon & Breach Science Publishers, New York, 1986

19.
P. N. Rathie and H. G. Rohrer, The exact distribution of products of independent random variables, Metron 45 (1987), no. 3-4, 235-245

20.
A. M. Rugman, International Diversification and the Multinational Enterprise, Lexington, 1979

21.
H. Sakamoto, On the distributions of the product and the quotient of the independent and uniformly distributed random variables, Tohoku Math. J. 49 (1943), 243-260

22.
S. M. Shcolnick, On the ratio of independent stable random variables, Stability problems for stochastic models (Uzhgorod, 1984), 349-354, Lecture Notes in Math., 1155, Springer, Berlin, 1985

23.
M. D. Springer and W. E. Thompson, The distribution of products of beta, gamma and Gaussian random variables, SIAM J. Appl. Math. 18 (1970), 721-737 crossref(new window)

24.
B. M. Steece, On the exact distribution for the product of two independent beta-distributed random variables, Metron 34 (1976), no. 1-2, 187-190

25.
A. Stuart, Gamma-distributed products of independent random variables, Biometrika 49 (1962), 564-565 crossref(new window)

26.
J. Tang and A. K. Gupta, On the distribution of the product of independent beta random variables, Statist. Probab. Lett. 2 (1984), no. 3, 165-168 crossref(new window)

27.
C. M. Wallgren, The distribution of the product of two correlated t variates, J. Amer. Statist. Assoc. 75 (1980), no. 372, 996-1000 crossref(new window)