<p>One important mortality measure in life-table analysis is the probability of death estimated as the ratio of the number of deaths observed in a given period of time to the number of individuals at risk of death at the beginning of that period. A major analytical problem in many calculations based on survival data is the right-censorship that arises when data on certain survival times are not available during analysis. When the probabilities of death need to be estimated, e.g., in actuarial mortality tables, it is often assumed that the right-censored observations contribute in half to the number of individuals at risk. Unfortunately, the assumption leads to biased estimates of respective probabilities. In the paper, a new class of estimators of life-table probabilities in the model of random, independent and observable right-censorship is considered. The estimation is based on the sequential random sample. The proposed approach provides nonparametric and unbiased estimates of main mortality quantities, i.e.&#xa0;probabilities of death and, consequently, probabilities of survival. Based on these quantities other life-table statistics are also derived, i.e. the numbers of deaths and survivors, assuming the appropriate radix when necessary. The usefulness of this approach for developing so-called actuarial select mortality tables is illustrated.</p>