Characterization of hazard function factorization by Fisher information in minima and upper record values
The hazard function is an important characteristic for the analysis of reliability data. It is therefore of interest to see under what conditions it can be expressed as the product of a function of the variable and a function of the parameter. We show that such a factorization can be characterized by the property of Fisher information in minima and upper record values. We present similar results for the reversed hazard rate by the property of Fisher information in maxima and lower record values. These properties imply the characterization of two classes of exponential families.
Volume (Year): 72 (2005)
Issue (Month): 1 (April)
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- Glenn Hofmann, 2004. "Comparing the Fisher information in record data and random observations," Statistical Papers, Springer, vol. 45(4), pages 517-528, October.
- Gertsbakh, Ilya & Kagan, Abram, 1999. "Characterization of the Weibull distribution by properties of the Fisher information under type-I censoring," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 99-105, March.
- Z. Abo-Eleneen & H. Nagaraja, 2002. "Fisher Information in an Order Statistic and its Concomitant," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(3), pages 667-680, September.
- Zheng, Gang & Gastwirth, Joseph L., 2001. "On the Fisher information in randomly censored data," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 421-426, May.
- Stepanov, A. V. & Balakrishnan, N. & Hofmann, Glenn, 2003. "Exact distribution and Fisher information of weak record values," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 69-81, August.
- Zheng, Gang, 2001. "A characterization of the factorization of hazard function by the Fisher information under Type II censoring with application to the Weibull family," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 249-253, April.
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