Abstract The concept of inverting a normal probability density function in order to provide practitioners with realistic loss functions was introduced by Spiring [2]. Further developments saw the inversion of other density functions in an attempt to provide a variety of loss functions that could be used in depicting losses associated with deviations from a target (Spiring and Yeung [3]), Leung and Spiring [1]). The recent focus has been on the development and application of particular loss functions and their associated Risk functions. In this manuscript several properties associated with the entire family of Inverted Probability Loss Functions (IPLF) are investigated and outlined. As well, several IPLFs which possess interesting and unique properties associated with assessing, and depicting losses and loss functions are discussed. Several IPLFs will be considered, some plausible conjugate distributions presented and the general performance compared numerically under homogeneous conditions. Industrial examples demonstrating economic and monetary losses are included.
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