The strong law for the integral of P-L estimate under left truncation and right censoring

For left truncated and right censored model. let F-n be the product-limit estimate and phi a nonnegative measurable function. The almost sure limits of the cumulative hazard function based on F-n and the integral integral phi dF(n) are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.Mathematics, AppliedMathematicsSCI(E)EI0ARTICLE101253-12604