Cumulative Inaccuracy Research Articles

Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics

In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.

On weighted cumulative past (residual) inaccuracy for record values

In this paper, we propose the weighted cumulative past (residual) inaccuracy for record values. For this concept, we obtain some properties and characterization results such as relationships with other reliability functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of this weighted measure are considered. We also study a problem of estimating the weighted cumulative past inaccuracy by means of the empirical cumulative inaccuracy for lower record values.

Cumulative Measure of Inaccuracy and Mutual Information in k-th Lower Record Values

In this paper, we discuss the cumulative measure of inaccuracy in k-lower record values and study characterization results of dynamic cumulative inaccuracy. We also present some properties of the proposed measures, and the empirical cumulative measure of inaccuracy in k-lower record values. We prove a central limit theorem for the empirical cumulative measure of inaccuracy under exponentially distributed populations. Finally, we analyze the mutual information for measuring the degree of dependency between lower record values, and we show that it is distribution-free.

Quantile-based cumulative inaccuracy measures

Numerous statistical models do not have explicitly known distribution functions. Because of this, the study of properties of the cumulative residual (past) inaccuracy measures using distribution function-based approach are difficult. Further, it is well-known that in modeling and analyzing statistical data, an equivalent alternative to distribution function is quantile function. The objective of this paper is to introduce and study quantile versions of the cumulative residual (past) inaccuracy measures and their dynamic forms. We obtain some bounds, relations with other quantile-based reliability measures, monotonicity results and characterizations. Various examples are provided to show the importance of the proposed quantile-based measures and the associated results.

Results on Cumulative Measure of Inaccuracy in Record Values

In this paper, we propose cumulative measure of inaccuracy in lower record values and study characterization results in case of dynamic cumulative inaccuracy. We also discuss some properties of the proposed measures. Finally, we study a problem of estimating the cumulative measure of inaccuracy by means of the empirical cumulative inaccuracy in lower record values.

An Extension of Weighted Cumulative Inaccuracy Measure Based on Doubly Truncation

In the present communication, based on two extensions of Shannon entropy cumulative entropy by Rao, et al, 2004 and Kerridge’s inaccuarcy by Kerridge, (1961), we study and obtain some properties of weighted cumulative residual (past) inaccuracy for truncated random variables.‎ Several properties, including monotonicity, bounds and their connections to proportional (reversed) hazard model are obtained for left, right and doubly truncated random variables.‎ ‎‎ ‎