## Calculating travel time distribution parameters

Travel-time distribution
parameters are calculated by fitting the negative exponential trend line to the
cumulative distribution function of surveyed travel times. Exponential trend
lines can be fitted by many software packages, including Microsoft Office
Excel, which enables a visual display of the results and easy calculation of R^{2} values[8]. Values presented in this report have been
calculated using a least squares approximation, part of the Numerical Python
computing environment and accessed through the Python programming language. The
deterrence function is only calculated based upon the first 95% of data, as
attempting to fit sparsely placed higher values can severely distort the resulting
curve. An example of walking to home-based employment in MUAs is shown in figure
13.1; in this case the λ parameter is shown to be 0.065

Figure 13.1 MUA employment
(home-based) walking travel time distribution function

The raw data (distribution of trip times) shown
in figure 14.1 highlights an apparent categorisation of trip times by NZHTS
respondents. It reveals the majority of NZHTS respondents have rounded their
trip duration to the nearest five minutes, eg ‘my trip took 15 minutes’ rather
than accurately recording the trip time to the nearest minute. Accurate
recording of trip duration to the nearest minute would reveal a smoother
distribution of trip times more akin to the negative exponential trend line
fitted to the data.