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Distributions

Define distributions​

It is possible to create parametric distributions of seven types: uniform, normal, log-normal, log-logistic, exponential, Weibull, and gamma.

Parameters are specified in the top right corner, and may be provided in one of two formats: through the average, variance, and translation, or through their distribution-specific parameters. Notice that due to the complexity of inverse formulas, the Weibull and gamma distributions may only be defined through their parameters. Once the distribution type and parameters are specified, the user may click Generate histogram in the bottom right corner of the window to see the histogram in the graph.

The definition of pure distributions may not be sufficient to represent railway delays. For this reason, some additional controls are provided allowing the user to customise distributions.

Start cut​

The user may wish to represent a phenomenon that has zero probability of taking place before a given time. In this case, it is possible to define a start cut. Specify the desired value from which the histogram should start in the start cut box. Cutting the initial part of a histogram will result in the removal of some bars from the histogram. Since the total probability represented by the histogram must always be equal to 100%, the removed probability will be redistributed on the whole histogram.

End cut​

Similarly, to define an end cut for the histogram, i.e. graphically cutting it on the right side instead of the left side, is possible. This feature may be used when a phenomenon never exceeds a given time. To apply the end cut, the user should specify a value after which the histogram will end in the end cut box. The end cut is also redistributed on the whole histogram.

Tail​

Delay distributions in railways are often observed to have long tails. For this reason, we provide the option to apply tails to distributions. First, the user should define the starting point as a relative tail, i.e., from which percentile it should start. Then, the user should specify where the tail should end (and, consequently, how long it is). This value may only be specified as a fixed value (i.e. value of the x-axis).

Import Distributions​

Distributions can be imported from R.

Generate distributions from real data​

If analysis data is available the historic data can be used to automatically generate distributions.