Using distribution of data instead of data in `EstimatedDistribution`

Question

Because of huge amount of data, the data saved in their frequency. for example {1,1,1,1,1,1,2,2,1,2,2,1,1,2,1,2,1,3,24} saved as {{1,11},{2,6},{3,1},{24,1}} how can use this type of saved data in below command?

EstimatedDistribution[data,PowerDistribution[a,b],ParameterEstimator->"MaximumLikelihood"]

or

EstimatedDistribution[data,ZipfDistribution[a,b],ParameterEstimator->"MaximumLikelihood"]

Answer 1

You can use WeightedData[] for the purpose:

FindDistributionParameters[WeightedData @@ Transpose[{{1, 11}, {2, 6}, {3, 1}, {24, 1}}], 
                           PowerDistribution[a, b],
                           ParameterEstimator -> "MaximumLikelihood"]
   {a -> 0.041666666666666664, b -> 0.3657540721946402}