A Kind Of Order Statistics Distribution And It's Application

In small sample situation, examination sample whether obeys some same distribution, namely carries on the data compatible examination, literature [9] proposes thetest statistics 1≤i≤k≤m≤n to this question, in which .X₍₁₎ < X₍₂₎ <…< X_(n) is the order statistics of the independently identically dis-tributed sample X₁,…, X_n. In this paper, we promotes this result to 1≤s≤q≤p≤r≤n, and gives this test statistics density function of the integralexpression under the position scale parameter distribution f(x;μ,σ) = 1/σ((x-μ)/σ), then has given its precise distribution in the uniform distribution and under the exponential distribution situation, under the normal distribution has given the density approximate expression. Finally has given this test statistics in the armament system tentative data examination application, and has given the normal distribution compatibility inspection procedure and the example under the small sample situation.