![galton board galton board](http://i.ytimg.com/vi/PM7z_03o_kk/maxresdefault.jpg)
![galton board galton board](https://www.geogebra.org/resource/UgbRP7na/sBgBLo0lNNyyAzWH/material-UgbRP7na-thumb@l.png)
(A recent good recapitulation of the theory of Galton board and log-normal distribution can be found in Ref. c ′ and /c ′, the log-normal distribution will be generated.But if the deviation of the particle from one row to the next is a random multiplicative process with possible values If the deviation of the particle from one row to the next is a random additive process with possible values + c and − c, the normal distribution will be cre- ated by the board, which reflects the cumulative additive effects of the sequence of decision points. , the dynamics of such stochastic processes can be modeled as a particle falling down a board (such a board is called Galton board) and being deviated at decision points (the tips of the triangular obstacles) either left or right, see Fig. Before we present the main model, let us interpret the stochastic process yielding log-normal type distributions using the generative model method. In this paper, we propose a new car-following model inspired by the Galton board to explain this interesting phenomena. However, how these log-normal distributions are generated remained to be studied previously. It is clear that log-normal distribution model has smaller fitting errors.
![galton board galton board](https://media.cheggcdn.com/media/5ca/5caea529-a392-4c7b-97a7-9e895ede5295/phpacVamt.png)
Figure 1 shows the comparison results for the empirical, super-statistical and log-normal distributions P ( τ ), where τ = t h / ⟨ t h ⟩, t h denotes the sampled time-headways and ⟨ t h ⟩ is its mean value. μ and σ denote the mean and variance of the sampling data.