Criteria for the existence of a minimum contrast estimate from a pooled grouped data are discussed. The minimum contrast estimate from the pooled grouped data covers both the maximum likelihood estimate and the minimum chi-square estimate from the grouped data as a special case. These criteria can be drived by a method called probability contents boundary analysis. This method gives systematically sufficient, or necessary and sufficient conditions for the existence of minimum contrast estimates for a wide class of families of distributions. Resulting criteria do not depend on the form of underlying distribution function.