Ridits right, left, center, native and foreign

Ridit functions are specified with respect to an identified probability distribution. They are like ranks, only expressed on a scale from 0 to 1 (for unfolded ridits), or -1 to 1 ( for folded ridits). Ridit functions have generalised inverses called percentile functions. A native ridit is a ridit of a variable with respects to its own distribution. Native ridits can be computed using the ridit() function of Nick Cox's SSC package egenmore. Alternatively, weighted ridits can be computed using the SSC package wridit. This has a handedness() option, where handedness(right) specifies a right--continuous ridit (also known as a cumulative distribution function), handedness(left) specifies a left--continuous ridit, and handedness(center) (the default) specifies a ridit function discontinuous at its mass points. wridit now has a module fridit, computing foreign ridits of a variable with respect to a distribution other than its own, specifying the foreign distribution in another data frame. An application of ridits is ridit splines, which are splines in a ridit function, typically computed using the SSC package polyspline. As an example, we may fit a ridit spline to a training set, and use it for prediction in a test set, using foreign ridits of an X-variable in the test set with respect to the distribution of the X-variable in the training set. The model parameterss are typically values of an outcome variable corresponding to percentiles of the X-variable in the training set. This practice stabilises (or Winsorises) outcome values corresponding to X-values in the test set outside the range of X-values in the training set