On Some Transforms of Distribution Functions and their Relationships

Abstract

Some interrelationships between various transforms like total time on test, the density quantile function, the score function, the exponential function and the failure rate quantile function are surveyed. These relationships are employed to establish some characterization results of distribution functions. Some formulae for the transforms of distribution functions, often used in nonparametric statistics and survival analysis, are also presented to illustrate these relationships.

Keywords:

• Total time on test
• reliability
• dispersive ordering