A bivariate density function, without location parameter, is defined over the range 0< × < y <∞. The marginal distribution ofYis taken to be Stacy's generalized Gamma distribution [10], and the determining conditional distribution ofXis assumed to be the Beta distribution, normalized over the interval 0<x<y.Parameter estimation for the resulting five-parameter bivariate density, from a complete bivariate sample (xi, yi),i= 1, 2, …,n, is indicated. Whenever the parameters of the conditional Beta distribution may be assumed known, a technique for estimating the three parameters of Stacy's distribution from a complete sample of the warning-times,xi,i= 1, 2, …,n, is presented. Measures of the dispersion of the scale parameter estimates, when calculated from the sample of warning-times, are provided. In conclusion, some important special cases of the bivariate density are discussed.