In this paper, we introduce a novel way to quantify the remaining inaccuracy of order statistics by utilizing the concept of extropy. We explore various properties and characteristics of this new measure. Additionally, we expand the notion of inaccuracy for ordered random variables to a dynamic version and demonstrate that this dynamic information measure provides a unique determination of the distribution function. Moreover, we investigate specific lifetime distributions by analyzing the residual inaccuracy of the first-order statistics. Nonparametric kernel estimation of the proposed measure is suggested. Simulation results show that the kernel estimator with bandwidth selection using the cross-validation method has the best performance. Finally, an application of the proposed measure on the model selection is provided.

We introduce a new measure of inaccuracy based on extropy between distributions of the nth upper (lower) record value and parent random variable and discuss some properties of it. A characterization problem for the proposed extropy inaccuracy measure has been studied. It is also shown that the defined measure of inaccuracy is invariant under scale but not under location transformation. We characterize certain specific lifetime distribution functions. Nonparametric estimators based on the empirical and kernel methods for the proposed measures are also obtained. The performance of estimators is also discussed using a real dataset.

For monitoring purposes there is a need for a protocol to measure foot-pad dermatitis (FPD) on-farm. Therefore, we studied the effect of number of birds sampled, number of locations sampled and sampling location in a broiler house on the accuracy of measurement, in order to construct a protocol that can be applied in practice. Samples were taken from eight commercial flocks (Ross 308) at up to ten locations with up to 25 birds sampled per location. Foot-pad lesions were scored in all birds for both feet using the Swedish scoring method. No significant differences in FPD score were found between the first five birds and all birds sampled at a particular location. Although locations near the walls did not differ in FPD score from locations in the central area of a house, the severity of foot-pad lesions was unevenly distributed over the house. A model was constructed showing the inaccuracy related to the number of locations sampled in the house and the number of birds sampled per location. The model shows that in situations with at least five locations differences in inaccuracy are relatively small when a total of 100 birds or more is sampled. Inaccuracy is largest in a flock with variation in foot-pad scores, as compared to flocks with little variation. The results of this experiment can be used to determine the optimal sample size in a commercial broiler house.

Kerridge introduced a measure known as inaccuracy for complete probability distributions which is the generalisation of Shannon's entropy. In this paper we study a grouping property of the inaccuracy. Also we have established a coding theorem for personal codes by considering inaccuracy of order a and generalised mean length of order t under the condition .

The object of this paper is to characterize an information theoretic measure associated with three probability distributions known as ‘Information Improvement’ through a functional equation which arises by considering the additive property of the measure. This measure has been extensively used in economic analysis.