An Asymptotic Expansion Algorithm Of The Random Sample Quartiles Based On Cornish-Fisher Expansion

With the development of statistics, quartiles have been widely applied in the economic, engineering, and so on. Quartiles of known continuous distribution function for the random sample more easily obtained. However, in practical application and calculation, the random sample distribution function is often unknown or the form is very complex. So it is difficult to obtain an explicit expression, which leads to random sample of quartiles is difficult to determine.Based on Cornish-Fisher expansion, we proposed a random sample asymptotic expansion algorithm of the quartiles. With the quantiles of standard normal distribution and the former n-order cumulant of random samples, we discussed how to find the quantiles of a random sample of the distribution unknown and construct system reliability confidence interval in a reliability comprehensive assessment of the complex systems, and integrated by the example of Bayes methods of assessment of equipment reliability.