Claim: The asymptotic distributions of null quantile-transformed test statistics is the Null distribution in the procedure of hypothesis testing
Evidence: In statistical hypothesis testing, the null distribution is the probability distribution of the test statistic when the null hypothesis is true. The null distribution is defined as the asymptotic distributions of null quantile-transformed test statistics, based on marginal null distribution. Null distribution is a tool scientists often use when conducting experiments. The null distribution is the distribution of two sets of data under a null hypothesis. If the results of the two sets of data are not outside the parameters of the expected results, then the null hypothesis is said to be true. The null hypothesis is often a part of an experiment. In the procedure of hypothesis testing, one needs to form the joint distribution of test statistics to conduct the test and control type I errors. 
A statistical hypothesis is a hypothesis that is testable on the basis of observed data modeled as the realised values taken by a collection of random variables. A set of data is modelled as being realised values of a collection of random variables having a joint probability distribution in some set of possible joint distributions. The hypothesis being tested is exactly that set of possible probability distributions.