The statistical analysis of real world problems, is often affected by different type of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data (parameters). In other cases, the data may regard variations as in the quality control (tolerance limits), in financial data (opening value and closing value in a session), in temperature measurements (maximum and minimum values). The uncertainty in the data, which is strictly connected to the situations, 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.

Basic statistical methods for interval data / Lauro, Natale; Gioia, Federica. - In: STATISTICA APPLICATA. - ISSN 1125-1964. - STAMPA. - 17:(2005), pp. 1-17.

Basic statistical methods for interval data

LAURO, NATALE;
2005

Abstract

The statistical analysis of real world problems, is often affected by different type of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data (parameters). In other cases, the data may regard variations as in the quality control (tolerance limits), in financial data (opening value and closing value in a session), in temperature measurements (maximum and minimum values). The uncertainty in the data, which is strictly connected to the situations, 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.
2005
Basic statistical methods for interval data / Lauro, Natale; Gioia, Federica. - In: STATISTICA APPLICATA. - ISSN 1125-1964. - STAMPA. - 17:(2005), pp. 1-17.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/105830
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