\huge \begin{align*} &\text{Let } \hat{X} = \text{ Sample of non-negative R.V. } X \\ &\left\{ x_1, x_2 \ldots x_n \right\} = \text{ Unique values from } \hat{X} \\ &\left\{ f_1, f_2 \ldots f_n \right\} = \text{ Frequencies of each value } \\ \\ &\text{Define the} \text{ Cumulative Residual Entropy (CRE) of } \hat{X}: \\ &\mathcal{E}(\hat{X}) \triangleq \sum_{j=1}^{n-1} (x_{j+1} - x_{j}) r_j \log r_j \\ &\text{where } r_j \text{ is the } j^{th} \text{ value of the complement-cdf of } \hat{X}: \\ &r_j = 1 - \frac{1}{n}\sum_{k=1}^{j}f_k \text{ over interval } ( x_j, x_{j+1} ] \\ \end{align*}