A new least squares method for estimation and prediction based on the cumulative Hazard function

• Published in: AIMS mathematics Vol. 8; no. 9; pp. 21968 - 21992
• Main Authors: Aly, Amany E., El-Adll, Magdy E., Barakat, Haroon M., Aldallal, Ramy Abdelhamid
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: cumulative hazard function; generalized order statistics; least squares method; mean squared error; monte carlo simulation; pitman's measure of closeness
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.20231120

In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of Rényi representation. The method can be used with type Ⅱ right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the efficiency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods.