Authors' reply to "Comments on 'A New Model of Two Directional $J_{c}$ Distributions for Bi$_{2}$Sr $_{2}$CaCu$_{2}$ O$_{8}$ Materials'"

The authors agree to the point made by Nadarajah, et. al. that the model that employs the mixture of Gaussian distributions is not a new idea. However, the mixtures of Gaussian distribution was only used to clarify the relationship between the local critical current density (J
_c
) distribution and the microstructure of the samples to successfully explain the relationship between the local J
_c
distribution and the microstructure of the Bi2212 materials. Because the local J
_c
distributions are directly connected to the electric fields versus current density (E-J) characteristics, the model permits the interpretation of the complicated E-J properties by means of the microstructures.