The Shapes of a Probability Density Function and Its Hazard Function
The shape of a probability density function restricts that of its hazard function, and vice versa. We are concerned with the six specific ‘shapes’: increasing, decreasing, unimodal, anti-unimodal, increasing-decreasing-increasing, and decreasing-increasing-decreasing.
KeywordsProbability Density Function Hazard Function Distribution Range Finite Interval Discontinuous Point
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Efron, B. and Johnstone, I.M. (1990) “Fisher’s information in terms of the hazard rate”, Annals of Statistics
, 18, 38–62.MathSciNetMATHCrossRefGoogle Scholar
Lawless, J.F. (1982) Statistical Models and Methods for Lifetime Data
, New York, NY: Wiley.MATHGoogle Scholar
Sibuya, M. (1984) “ Unimodal hazard functions,” Japanese Journal of Applied Statistics
, 13, 115–124. (in Japanese)CrossRefGoogle Scholar
Sibuya, M. (1994) “ Unimodal and anti-unimodal hazard function,” (in preparation).Google Scholar
Zelterman, D. (1992) “ A statistical distribution with an unbounded hazard function and its application to a theory from demography,” Biometrics
, 48, 807–818.CrossRefGoogle Scholar
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