ON THE PRODUCT AND RATIO OF GAMMA AND WEIBULL RANDOM VARIABLES

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this note, the exact distributions of the product XY and the ratio X/Y are derived when X and Y are gamma and Weibull random variables distributed independently of each other.The authors thank the referee and the editor for carefully reading the paper and for their help in improving the paper.

[1]  S. Nadarajah,et al.  On the Product and Ratio of t and Logistic Random Variables , 2004 .

[2]  T. Pham-Gia,et al.  Distributions of the ratios of independent beta variables and applications , 2000 .

[3]  P. Korhonen,et al.  The probability distribution of the ratio of the absolute values of two normal variables , 1989 .

[4]  H. J. Malik,et al.  Probability Density Function of the Product and Quotient of Two Correlated Exponential Random Variables , 1986, Canadian Mathematical Bulletin.

[5]  D. L. Hawkins,et al.  Bivariate distributions of some ratios of independent noncentral chi-square random variables , 1986 .

[6]  S. M. Shcolnick,et al.  On the ratio of independent stable random variables , 1985 .

[7]  Jen Tang,et al.  On the distribution of the product of independent beta random variables , 1984 .

[8]  C. G. Khatri,et al.  The distribution of product of independent beta random variables with application to multivariate analysis , 1981 .

[9]  Cheryl M. Wallgren The Distribution of the Product of Two Correlated t Variates , 1980 .

[10]  A. Rugman,et al.  International diversification and the multinational enterprise , 1979 .

[11]  Horst Podolski THE DISTRIBUTION OF A PRODUCT OF n INDEPENDENT RANDOM VARIABLES WITH GENERALIZED GAMMA DISTRIBUTION , 1972 .

[12]  Robert H. Lochner,et al.  On the Distribution of the Ratio of Two Random Variables Having Generalized Life Distributions , 1971 .

[13]  M. Feldstein,et al.  THE ERROR OF FORECAST IN ECONOMETRIC MODELS WHEN THE FORECAST-PERIOD EXOGENOUS VARIABLES , 1971 .

[14]  M. Springer,et al.  The Distribution of Products of Beta, Gamma and Gaussian Random Variables , 1970 .

[15]  S. James Press,et al.  The t-Ratio Distribution , 1969 .

[16]  H. Grubel Internationally Diversified Portfolios: Welfare Gains and Capital Flows , 1968 .

[17]  M. Springer,et al.  The Distribution of Products of Independent Random Variables , 1966 .

[18]  G. Marsaglia Ratios of Normal Variables and Ratios of Sums of Uniform Variables , 1965 .

[19]  A. Stuart Gamma-distributed products of independent random variables , 1962 .

[20]  H. Harter On the Distribution of Wald's Classification Statistic , 1951 .

[21]  H. Sakamoto,et al.  On the Distributions of the Product and the Quotient of the Independent and Uniformly Distributed Random Variables , 1943 .