ON THE PRODUCT AND RATIO OF GAMMA AND WEIBULL RANDOM VARIABLES
- 9 February 2006
- journal article
- other
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 22 (02), 338-344
- https://doi.org/10.1017/s0266466606060154
Abstract
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.Keywords
This publication has 16 references indexed in Scilit:
- Distributions of the ratios of independent beta variables and applicationsCommunications in Statistics - Theory and Methods, 2000
- Probability Density Function of the Product and Quotient of Two Correlated Exponential Random VariablesCanadian Mathematical Bulletin, 1986
- Bivariate distributions of some ratios of independent noncentral chi-square random variablesCommunications in Statistics - Theory and Methods, 1986
- On the distribution of the product of independent beta random variablesStatistics & Probability Letters, 1984
- The Distribution of the Product of Two Correlated t VariatesJournal of the American Statistical Association, 1980
- On the Distribution of the Ratio of Two Random Variables Having Generalized Life DistributionsTechnometrics, 1971
- The Error of Forecast in Econometric Models when the Forecast-Period Exogenous Variables are StochasticEconometrica, 1971
- The Distribution of Products of Beta, Gamma and Gaussian Random VariablesSIAM Journal on Applied Mathematics, 1970
- The t-Ratio DistributionJournal of the American Statistical Association, 1969
- Ratios of Normal Variables and Ratios of Sums of Uniform VariablesJournal of the American Statistical Association, 1965