Fisher-Based Inaccuracy Information Measure

We introduce a new inaccuracy measure in terms of Fisher information. The proposed information measure is referred to as Fisher-based inaccuracy information (FBII) measure. Next, we examine some properties of this information measure and specifically examine it for escort and equilibrium distributions. Further, we propose Bayes–Fisher-based inaccuracy information (BFBII) measure and examine its connection to Kullback–Leibler and chi-square divergence measures. Moreover, in three different optimization problems, we show that the harmonic-mixture distribution gives optimal information based on BFBII measure. Some examples of FBII measure and escort density related to skew-normal and Student-t distributions are also illustrated, and then are applied to fish condition factor time series.