Reconstruction of the past lower record values in a proportional reversed hazard rate model

Abstract

In this paper, the situation in which some lower records from a proportional reversed hazard rate model (PRHRM) are lost at the beginning of the experiment is considered. The reconstruction problem of the past lower records based on observed records from a PRHRM is discussed. Several various methods are used to obtain point reconstructors. More details are given for the Fréchet distribution. Three reconstruction intervals are also obtained and compared in the sense of the expected width for the case of Fréchet distribution. A data set representing the annual flood loss is applied to illustrate the proposed procedure in this paper. Eventually, some concluding remarks are presented.

Keywords:

• best unbiased conditional reconstructor
• highest conditional density reconstruction interval
• Fréchet distribution

Mathematics Subject Classifications:

• Primary: 62F10
• Secondary: 62F25

Acknowledgements

The authors thank the associate editor and two referees for their helpful comments and suggestions which improved the presentation of the paper considerably. Partial support from Ordered and Spatial Data Center of Excellence of Ferdowsi University of Mashhad is acknowledged.