Inferences about the scale parameter of the gamma distribution based on data mixed from censoring and grouping

This paper studies the MLE of the scale parameter of the gamma distribution based on data mixed from censoring and grouping when the shape parameter is known. The study shows that under Type I mixed data, the MLE of the scale parameter exists, is unique, and converges almost surely to the true value provided the number of items that fail in the last interval is less than the total number of items placed on test. Under Type II mixed data, these properties hold unconditionally. The relationship between the MLE's based on mixed data and censored data is also examined. An upper bound on the MLE under both Type I and II mixed data is derived to simplify the search for the MLE.