Strong consistency for delta sequence ratios

Almost sure convergence for ratios of delta functions establishes global and local strong consistency for a variety of estimates and data generations. For instance, the empirical probability function from independent identically distributed random vectors, the empirical distribution for univariate independent identically distributed observations, and the kernel hazard rate estimate for right-censored and left-truncated data are covered. The convergence rates derive from the Bennett-Hoeffding inequality.