F. Seilliermoiseiwitsch, SEQUENTIAL PROBABILITY FORECASTS AND THE PROBABILITY INTEGRAL TRANSFORM, International statistical review, 61(3), 1993, pp. 395-408
The probability integral transform and its conditional version provide
us with means of assessing the performance of statistical forecasting
systems. The distributional characteristics of the residuals are cons
idered under both the assumed sampling model and the probability model
induced by the forecasting system. The CPIT can also serve as a tool
to generate predictive distributions.