Abstract: The probability distribution of the τ variable,the distribution of its limit and the principal numerical characteristics are firstly studied.The method and formulars for calculating the distribution density of the probability of the variable are derived.The distribution of limit of τ variable,being considered as normal-variable,is proved and its-functional value has been calculated.Base on the above theoretical derivation and numerical calculation,the application of the τ variable for the statistical test on outliers and curve fitting are discussed.