The number " z " follows from the cumulative distribution function, in this case the cumulative normal distribution function:
2.
Another commonly applied model is the probit model where F is the cumulative normal distribution function, \ lambda = 0 and e follows a binomial distribution.
3.
Here, the step size is the inverse cumulative normal distribution \ Phi ^ {-1 } ( z, \ mu, \ sigma ) where 0 d " " z " d " 1 is a uniformly distributed random number, and ? and ? are the mean and standard deviations of the normal distribution, respectively.
4.
For the special case where ? is equal to zero, after " n " steps, the translation distance's probability distribution is given by " N " ( 0, " n " ? 2 ), where " N " ( ) is the notation for the normal distribution, " n " is the number of steps, and ? is from the inverse cumulative normal distribution as given above.
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