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tokens: the inverse time axis and divide the result by 2 to obtain an overall weighted summation versus time, . The maximum value of the obtained overall weighted summation yields the mirror time delay estimation , . Figure 2 plots 5, 8, and 11 illustrate the results from the mirror time delay estimator for , respectively. Among the three mirror time delay estimations, we choose (Figure 2 ; plot 5) since it follows the form of the basic definition in statistics and also shows high performance results (Section 3.5 ). We use the rest of the results for reliability testing of our time delay estimation, as we will describe later in this section. 5. Weighted average correlation, : To check the reliability of the estimated time delay, we will need a normalized maximum weighted summation (between −1 to +1). This can ensure that the best estimated time delay corresponds to a reasonable correlation between the two light curves. Dividing the maximum weighted summation of correlations by the sum of the corresponding weights yields weighted average correlations in the form ofand similarlyand also for the mirror estimator we havewhere the above equations are valid for , and the weighted average correlations have values in the range of . It is worth noting that using the weighted summation of correlations instead of the weighted average correlation enables us to consider the number of segments of data that contribute in the estimation of the best time delay. This gives more weights to time delays that are derived using more segments of the data, in comparison to time delays that are derived by considering only one or two segments of data. Therefore, we obtain the best time delay using the maximum weighted summation, while the weighted average correlation shows the reliability of the estimation. We see in our analysis that this approach can improve our analysis by minimizing the possibility of having any outliers in our results. 6. Reliability test: To check the reliability of the time delay estimation, we consider several criteria. First we follow Aghamousa Shafieloo ( 2015 ) in assigning and and () as an acceptance limit for correlation values. Next we check the consistency of each pair of , time delays by checking their sign. We expect the consistent pairs have opposite signs. In addition, we calculate the mean and standard deviations of the absolute values of three , time delay pairs and expect the reliable results to show a low discrepancy with days and . If any of the above conditions is not satisfied, we consider our method disqualified to attain a reliable time delay estimation for the case of study. Figure 2. Plots 1 and 2 show the weighted correlation coefficients and for seven data segments and smooth fit segments for the lensed quasar SDSS J1001+5027 light curve data, respectively. Plots 3, 6, and 9 represent the weighted summations, that is, , which are calculated from the weighted correlation coefficients shown in plot 1 using three different