Interval statistic and its distribution

Interval statistics and interval rank statistics are presented respectively, and their distributions and united distributions are derived. Not only the means, the variances and the covariances of interval statistics, but also the mean ranks, the median ranks and the percent ranks of interval rank statistics are given. Interval statistics and order statistics can complement each other, and the information among order statistics can fully be exploited and applied by interval statistics. Then the best linear unbiased estimate method for interval data of normal distribution, Weibull distribution, extreme value distribution or other location-scale parameter models is presented. The presented method has higher precision, and solves the problem of reliability assessment with small sample of storage life.