  In this work, an independent and detailed statistical analysis of the
double-Chooz experiment is performed. To have a thorough understanding of the
implications of the double-Chooz data on both oscillation parameters
$\sin^{2}(2\theta_{13})$ and $\Delta m^2_{31}$, we decided to analyze the data
corresponding to the Far detector, with no additional restriction. By doing
this, confidence regions and best fit values are obtained for
($\sin^{2}(2\theta_{13}),\Delta m^2_{31}$). This analysis yields an
out-of-order $\Delta m^2_{31}$ minimum, which has already been mentioned in
previous works, and it is corrected with the inclusion of additional
restrictions. With such restrictions it is obtained that $\sin ^{2}(2 \theta
_{13})=0{.}084_{-0{.}028}^{+0{.}030}$ and $\Delta
m^2_{31}=2.444^{+0.187}_{-0.215} \times 10^{-3}$ eV$^2$/c$^4$. Our analysis
allows us to study the effects of the so called "spectral bump" around 5 MeV,
it is observed that a variation of this spectral bump may be able to move the
$\Delta m^2_{31}$ best fit value, in such a way that $\Delta m^2_{31}$ takes
the order of magnitude of the MINOS value. Finally, and with the intention of
understanding the effects of the preliminary Near detector data, we performed
two different analyses, aiming to eliminate the effects of the energy bump. As
a consequence, it is found that unlike the Far Detector analysis, the Near
detector data may be able to fully determine both oscillation parameters by
itself, resulting in, $\sin^2(2\theta_{13}) = 0.095 \pm 0.053$ and $\Delta
m^{2}_{31} = 2.63^{+0.98}_{-1.15} \times 10^{-3} \text{eV}^2 / \text{c}^4$. The
later analyses represent an improvement with respect to previous works, where
additional constraints for $\Delta m^2_{31}$ were necessary.
