Estimation of the Scale Parameter of Triangular Distribution Using Absolved Order Statistics
Estimation of the scale parameter of triangular distribution using AOS
Keywords:Triangular Distribution, Order Statistics, Absolved Order Statistics, Minimal Sufficient Statistics, Best Linear Unbiased Estimate, Estimation from Censored Samples, U-statistics
In this paper, a new set of ordered random variables called Absolved Order Statistics(AOS) from a scale dependent triangular distribution is considered. The vector of AOS is found to be the minimal sufficient statistic for the triangular distribution with scale parameter σ. Based on AOS, the best linear unbiased estimate ˆσ of σ along with its variance is explicitly derived. It is found that censoring based on AOS is more realistic and the estimate obtained from it for σ is more efficient than the case of censoring with order statistics. In this study, we also obtained the U-statistic estimator based on AOS for the scale parameter σ of the triangular distribution.