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There are various ways of describing intermittent features in space plasma turbulence, but we lack a unified paradigm to connect the results from these different approaches. In this work, we aim to construct a unified paradigm to describe various intermittency-related quantities with the same set of parameters. The Castaing function, which describes the scale-dependent turbulence amplitude as a logarithmic normal distribution, is adopted as a fitting function to describe the probability distribution of magnetic field difference at various timescales tau. Two fitting parameters (mu, lambda) as a function of tau are obtained and regarded as the fundamental information, based on which various characteristics related to intermittency can be derived at one time, e.g., the high-order structure functions, their scaling exponent as a function of the order, or the flatness as a function of tau. We find it is the derivative ratio, DR = d lambda(2)/d(ln tau)/d mu/d(ln tau), that determines the order trend of the scaling exponent zeta(m). A negative DR of a small absolute is responsible for a curved zeta(m) in the inertial range, and a large positive DR leads to a straight zeta(m) in the kinetic range. Therefore, it is suggested that the probability distribution function of the magnetic increments spreads in width (lambda(tau)) with decreasing tau in the inertial range, while it is saturated and even slightly reduced in the kinetic range. Moreover, it is found that the turnings between the inertial and kinetic scales for the two Castaing fitting parameters mu(tau) and lambda(2)(tau) occur at different scales: ln tau similar to 0 and ln tau similar to 2, respectively. The reason for this different behavior is still unclear.
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