Histogram Cumulative

Histogram Cumulative statistics record the time-evolution of the cumulative histogram data when a Histogram feature is enabled. The cumulative range and bin resolution are defined by the Histogram feature in the model tree. This output produces a tab-separated ASCII .txt file named HistogramCumulative_{DynamicName}.txt, where the dynamic name matches the feature name in the Model Tree.

The output file contains columns corresponding to the bin center values defined by the histogram configuration. The first row of the file lists these bin center values, which represent the value of the underlying variable (normalized from 0 to 1). This row defines the independent variable. Each subsequent row correspond to the cumulative fraction of values less than or equal to each bin location over time. These rows define the dependent variable, giving the cumulative distribution of the variable at each time. Each row in the output file corresponds to a new statistics output time and is appended at the Statistics Output Write Interval.

Unlike a standard Histogram, each row forms a Cumulative Distribution Function (CDF), meaning the values are monotonically increasing from 0 to 1 across the bins. To correctly interpret or visualize this data, the cumulative fraction should be treated as the vertical axis (y-axis), while the corresponding bin values (the variable values) should be treated as the horizontal axis (x-axis). In this representation, the y-axis gives the fraction of the domain with values below a specified threshold, and the x-axis gives that threshold value. For example, a cumulative value of 0.5 at a given bin indicates that 50% of the domain has values less than or equal to the corresponding bin-center value. Similarly, a cumulative value of 0.9 indicates that 90% of the domain lies at or below that value, and 10% exceeds it.

The index table below shows the statistics that will appear in the Cumulative Histogram output file. Within this table, each statistic corresponds to a column in the output table which evolves with the time column.

Tip

Users sometimes plot the bin values on the y-axis and the cumulative fraction on the x-axis, which inverts the interpretation and leads to confusion. The correct interpretation is always: x-axis = variable value, y-axis = cumulative fraction.

Statistics	Units	Details	When Appears
Time	s	simulation time
Values	Dimensionless	cumulative histogram values