CumDist - Custom continuous distribution using cumulative probabilities
CumDist(P, R: Array[I]; I: Index)
The CumDist function represents a distribution having a Cdf passing through the indicated points (as given by «P» and «R»), and using a monotonic cubic interpolation the the Cdf between those points. The monotonic cubic interpolation creates a smooth Cdf, so that the Pdf is also continuous.
«P» must be non-decreasing, «R» must be strictly increasing, and both must be indexed by «I». If index «I» is omitted, «R» must be a valid index and «P» must be indexed by «R».
The user guide contains an error. It states that CumDist uses linear interpolation on the Cdf. This is not correct, and doing so would result in a discontinuous Pdf. [EW 4992]
Optional parameters
Smooth
By default, CumDist performs a monotonic cubic interpolation on the Cdf, which ensures that the Cdf is smooth and the Pdf is continuous. (Note: The Analytica user guide has long contained an error on this point where it incorrectly claims that CumDist uses linear interpolation on the Cdf).
An optional parameter, «Smooth», can be set to False to use linear interpolation on the Cdf, resulting in a piecewise linear [[Cdf] and a piecewise constant (but discontinuous) PDF. For example:
CumDist(P, R, I, Smooth: false)
Over
To generate independent samples for each combination of element across a set of indexes, use the «Over» parameter, e.g.:
CumDist(P, R, I, Over: Time)
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