The TRIBUT procedure is based on the assumption that each vehicle has its individual time value VT. VT is a random variable that is log-normal distributed with the parameters σ (dispersion parameter) and µ (position parameter).
VT ~ LN(µ,σ2)
The logarithmic normal distribution is characterized by the following properties:
- The median M of the logarithmic normal distribution is
. 50% of all users use a higher time value than M, and the other 50% of users use a lower time value than M. - The expected value E is calculated as follows:
. - The maximum of the probability density function (mode) is fmax = eµ-σ2.
- The standard deviation of the logarithmic normal distribution is:
. - The probability is equal to zero for negative values.
The figures show the density function (Illustration 109) and the distribution function (Illustration 110).
Logarithmic normal distributions
Illustration 109: Density function
