The stationary sound level is measured as the point of subjective equality (PSE) to the randomly fluctuating sound in loudness discrimination. The fluctuating stimulus is specified with two parameters : fluctuating width and velocity. These are obtained from the distribution curve of the stimulus sound envelope. The stimuli presentation are carried out using stochastic approximation method where the level of the stationary sound is varied sequentially in each test based on the observation of each response. As a result of these tests, a PSE is roughly estimated. The final step is to determine a more accurate PSE through numerical techniques. The results indicate that subjects hear sounds louder as the fluctuation width and velocity are relatively increased. A nonlinear temporal integration model is used to simulate the hearing system. Several frequently occuring levels appear in the model's output (a model of loudness) distribution curve. The average of these levels closely correlates to the calculated PSE.