Summary: A self-consistent algorithm was proposed by B.W. Turnbull
[J. Am. Stat. Assoc. 69, 169-173 (1974; Zbl 0281.62044
)] to estimate the distribution of
on the basis of interval censored data of
. An interval censored
is known either to lie inside an interval
, or to lie below
. The calculation of the estimates is not an easy task. In this article, an urn model is constructed to sample the random intervals and to calculate relevant probabilities. It is proved that using the interval data obtained from the urn model, consistent estimates can be obtained by using the self-consistency algorithm. A simulation example is provided to illustrate the procedure.