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The newly released observational $H(z)$ data (OHD) is used to constrain$\Lambda(t)$CDM models as holographic and agegraphic dark energy. By the use ofthe length scale and time scale as the IR cut-off including Hubble horizon(HH), future event horizon (FEH), age of the universe (AU), and conformal time(CT), we achieve four different $\Lambda(t)$CDM models which can describe thepresent cosmological acceleration respectively. In order to get a comparisonbetween such $\Lambda(t)$CDM models and standard $\Lambda$CDM model, we use theinformation criteria (IC), $Om(z)$ diagnostic, and statefinder diagnostic tomeasure the deviations. Furthermore, by simulating a larger Hubble parameterdata sample in the redshift range of $0.1<z<2.0$, we get the improvedconstraints and more sufficient comparison. We show that OHD is not only ableto play almost the same role in constraining cosmological parameters as SNe Iadoes but also provides the effective measurement of the deviation of the DEmodels from standard $\Lambda$CDM model. In the holographic and agegraphicscenarios, the results indicate that the FEH is more preferable than HHscenario. However, both two time scenarios show better approximations to$\Lambda$CDM model than the length scenarios.

Constraints on $\Lambda(t)$CDM models as holographic and agegraphic dark energy with the observational Hubble parameter data