Turnbull estimation

Turnbull1, 2 developed an iterative algorithm to compute a nonparametric maximum likelihood estimate of the cumulative distribution function for the data. This method applies to more general situations, for example, where the intervals are overlapping.

Minitab displays output summarizing the Turnbull estimate of the interval probabilities, along with standard errors for these probabilities.


  1. B.W. Turnbull (1976). "The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data," Journal of the Royal Statistical Society 38, pp. 290-295.
  2. B.W. Turnbull (1974). "Nonparametric Estimation of a Survivorship Function with Doubly Censored Data," Journal of the American Statistical Association 69, 345, pp. 169-173.
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