Estimation of the Scale Parameter of Triangular Distribution Using Absolved Order Statistics

Estimation of the scale parameter of triangular distribution using AOS

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

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.