One-sided estimating and testing problems for scale models from grouped samples

This article mainly analyzes estimating and testing problems for scale models from grouped samples. Suppose the support region of a density function, which does not depend on parameters, is divided into some disjoint intervals, grouped samples are the number of observations falling in each intervals respectively. The studying of grouped samples may be dated back to the beginning of the century, in which only one sample location and/or scale models is considered. (Shi, N.-Z., Gao, W., Zhang, B.-X. (2001). One-sided estimating and testing problems for location models from grouped samples. Comm. Statist.-Simul. Comput. 30(4)) had investigated one-sided problems for location models, this article discusses one-sided estimating and testing problems for scale models. Some algorithms for obtaining the maximum likelihood estimates of the parameters subject to order restrictions are proposed.