Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In statistics, the probability integral transform or transformation relates to the result that data values that are modelled as being random variables from any given continuous distribution can be converted to random variables having a uniform distribution. This holds exactly provided that the distribution being used is the true distribution of the random variables; if the distribution is one fitted to the data the result will hold approximately in large samples. Suppose that a random variable X has a continuous distribution for which the cumulative distribution function is F. One use for the probability integral transform in statistical data analysis is to provide the basis for testing whether a set of observations can reasonably be modelled as arising from a specified distribution. Specifically, the probability integral transform is applied to construct an equivalent set of values, and a test is then made of whether a uniform distribution is appropriate for the constructed dataset.