A Modified Chi‐squared Approach for Fitting WEIBULL Models to Synthetic Life Tables¹

WEIBULL models are fitted to synthetic life table data by applying weighted least squares analysis to log log functions which are constructed from appropriate underlying contingency tables. As such, the resulting estimates and test statistics are based on the linearized minimum modified X²₁‐criterion and thus have satisfactory properties in moderately large samples. The basic methodology is illustrated in terms of an example which is bivariate in the sense of involving two simultaneous, but non‐competing, vital events. For this situation, the estimation of WEIBULL model parameters is described for both marginal as well as certain conditional distributions either individually or jointly.