Race Levy-Brownian model: An evidence accumulation model with both Levy flight and diffusion properties

Recently, Levy Flight models have attracted much attention. The main reason for their outstanding performance in modeling human behavior is considering a heavy-tailed distribution for the noise of the accumulation process which causes some sudden jumps during the accumulation process. But it is worth mentioning that when the distribution of noise of the accumulation tends to a more heavy-tailed distribution, low values of the noise are less likely to happen, and then the accumulation process between two jumps is less noisy than in the diffusion model. Consequently, in the Levy Flight models, large sudden jumps and low-value noises can not happen simultaneously. Thus, it is not so realistic, because we have both low values of noise and also some jumps during the accumulation process. In contrast with the previous evidence accumulation models that include only one noise distribution, the Levy-Brownian model utilizes both Gaussian and Levy white noises simultaneously in a way that the noise of the accumulation process is a weighted summation of the Gaussian (its weight is equal to lambda) and the Levy (its weight is equal to 1). Therefore, this model is the general form of the Levy Flight model and when lambda is equal to zero, this model is reduced to the Levy Flight model. Considering such a hybrid distribution yields an accumulation process that has both lo value noises and some sudden large jumps at the same time. We have tested the performance of this model on some perceptual and lexical decision tasks and the obtained results exhibit a better performance of the model in comparison with the Levy Flight and diffusion models.