We present a statistical study of the nonthermal X-ray emission of 27 young rotation-powered pulsars (RPPs) and 24 pulsar wind nebulae (PWNe) using the Chandra and XMM-Newton observations, whose high spatial resolutions enable us to resolve pulsars from their surrounding PWNe. We obtain the X-ray luminosities and spectra separately for RPPs and PWNe, and then investigate their distribution and relation to each other, as well as their relation to the pulsar rotational parameters. In pair-correlation analysis we find that (1) the X-ray (2-10 keV) luminosities of both pulsar and PWN (L_(X,psr) and L_(X,pwn)) display a strong correlation with the pulsar spin-down power E and characteristic age τ. The scalings resulting from a simple linear fit to the data are L_(X,psr) ∝ E~(0.92±0.04) and L_(X,pwn) ∝ E~(1.45±0.08) (68% confidence level), respectively; however, neither fit is statistically acceptable. (2) L_(X,psr) also shows a possible weak correlation with the pulsar period P and period derivative P, whereas L_(X,pwn) manifests a similar weak correlation with P only. (3) The PWN photon index Γ_(pwn) is positively correlated with L_(X,pwn) and L_(X,pwn)/E. We also found that the PWN X-ray luminosity is typically 1 to 10 times larger than that from the underlying pulsar, and the PWN photon indices span a range of 1.5 approx< Γ_(pwn) approx< 2.1. The statistical study of PWN spectral properties supports a particle wind model in which the X-ray-emitting electrons are accelerated by the termination shock of the wind.
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