We have studied the enhancement of spontaneous emission rates for InAs quantum dots embedded in GaAs microdisks in a time-resolved photoluminescence experiment. Inhomogeneous broadening of the quantum dot energy levels and random spatial distribution of the quantum dots in a microdisk lead to a broad distribution of the spontaneous emission rates. Using a nonnegative least-norm algorithm, we extract the distribution of spontaneous emission rates from the temporal decay of emission intensity. The maximum spontaneous emission enhancement factor exceeds 10.