Trimmed regions induced by parameters of a probability Articles uri icon

publication date

  • May 2012

start page

  • 306

end page

  • 318

volume

  • 107

international standard serial number (ISSN)

  • 0047-259X

electronic international standard serial number (EISSN)

  • 1095-7243

abstract

  • Consider any kind of parameter for a probability distribution and a fixed distribution. We study the subsets of the parameter space constituted by all the parameters of the probabilities in the alfaalfa-trimming of the fixed distribution. These sets will be referred to as parameter trimmed regions. They are composed of all parameter candidates whose degree of suitability as such a parameter for the distribution is, at least, a specific value alfaalfa. In particular, we analyze location, scale, and location-scale parameters and study the properties of the trimmed regions induced by them. Several specific examples of parameter trimmed regions are studied. Among them, we should mention the zonoid trimmed regions obtained when the chosen parameter is the mean value and the location-scale regions of a univariate distribution obtained when the parameter is the pair given by the mean and the standard deviation.

keywords

  • alpha-trimming of a probability; depth function; location-scale depth; quantile trimming; zonoid trimming