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The accuracy and reliability of gamma-ray bursts (GRBs) as distanceindicators are strongly restricted by their systematic errors which are largerthan statistical errors. These systematic errors might come from eitherintrinsic variations of GRBs, or systematic errors in observations. In thispaper, we consider the possible origins of systematic errors in the followingobservables, (i) the spectral peak energies (Ep) estimated by Cut-off power law(CPL) function, (ii) the peak luminosities (Lp) estimated by 1 second inobserver time. Removing or correcting them, we reveal the true intrinsicvariation of the Ep-TL-Lp relation of GRBs. Here TL is the third parameter ofGRBs defined as TL ~ Eiso / Lp. Not only the time resolution of Lp is convertedfrom observer time to GRB rest frame time, the time resolution with the largestlikelihood is sought for. After removing obvious origin of systematic errors inobservation mentioned above, there seems to be still remain some outliers. Forthis reason, we take account another origin of the systematic error as below,(iii) the contamination of short GRBs or other populations. To estimate thebest fit parameters of the Ep-TL-Lp relations from data including outliers, wedevelop a new method which combine robust regression and an outlieridentification technique. Using our new method for 18 GRBs with {\sigma}Ep/Ep <0.1, we detect 6 outliers and find the Ep-TL-Lp relation become the tightestaround 3 second.

The Improved Ep-TL-Lp Diagram and a Robust Regression Method