Basic Statistical Methods for Interval Data

Real world data analysis is often affected by different type of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data (parameters). The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering, rather than a single value for each data, the interval of values in which it may fall: the interval data. This kind of data representation imposes a new formulation of the classical statistical methods in the case that interval-valued variables are considered. Accordingly, purpose of the present work is to develop suitable statistical methods for: obtaining a synthesis of the data, analysing the variability in the data and the existing relations among interval-valued variables. The proposed solutions are based on the following assessments: - The developed statistics for interval-valued variables are intervals. - Statistical methods for interval-valued variables embrace classical statistical methods as special cases. - The proposed interval solutions do not contain redundant elements with respect to a given criterion. In the present work particular interest is devoted to the proof of the properties of the proposed techniques and to the comparison of the obtained results with those already existing in the literature