Techniques are described for parallel processing of database queries with an inverse distribution function by a database management system (DBMS). To improve the execution time of a query with an inverse distribution function, the data set referenced in the inverse distribution function is range distributed among parallel processes that are spawned and managed by a query execution coordinator process (QC), in an embodiment. The parallel executing processes sort each range of the data set in parallel, while the QC determines the location(s) of inverse distribution function values based on the count of values in each range of the data set. The QC requests the parallel processes to produce to the next stage of parallel processes the values at the location(s) in the sorted ranges. The next stage of parallel processes computes the inverse distribution function based on the produced values. Techniques are also described for parallel executing of queries that may additionally include another inverse distribution function, one or more non-distinct aggregate functions and one or more distinct aggregate functions.