1. A method for coverage driven generation of stimuli for verification of a device-under-test (DUT), the method comprising: receiving from a user, via an input device, i) a constraint model with one or more entities for generating a set of random stimuli for input to the DUT and ii) a coverage model with one or more coverage items defining a coverage space for verification of the DUT; using a processor, identifying a coverage item from the one or more coverage items in the received coverage model and finding a corresponding entity from the one or more entities in the received constraint model corresponding to the identified coverage item; using a processor, translating a coverage requirement related to the identified coverage item into a distribution directive for influencing a distribution in the set of random stimuli; wherein the distribution directive includes subranges of ranges that are covered by the generated random stimuli and weights assigned to the subranges; using a processor, solving the constraint model with the distribution directive on the corresponding entity, to obtain the set of random stimuli with the distribution tuned over the weighted subranges for fast filling the coverage space; and using a processor, applying the set of random stimuli with the tuned distribution to the input of the DUT for verification of the DUT.