  An important body of quantitative linguistics is constituted by a series of
statistical laws about language usage. Despite the importance of these
linguistic laws, some of them are poorly formulated, and, more importantly,
there is no unified framework that encompasses all them. This paper presents a
new perspective to establish a connection between different statistical
linguistic laws. Characterizing each word type by two random variables, length
(in number of characters) and absolute frequency, we show that the
corresponding bivariate joint probability distribution shows a rich and precise
phenomenology, with the type-length and the type-frequency distributions as its
two marginals, and the conditional distribution of frequency at fixed length
providing a clear formulation for the brevity-frequency phenomenon. The
type-length distribution turns out to be well fitted by a gamma distribution
(much better than with the previously proposed lognormal), and the conditional
frequency distributions at fixed length display power-law-decay behavior with a
fixed exponent $\alpha\simeq 1.4$ and a characteristic-frequency crossover that
scales as an inverse power $\delta\simeq 2.8$ of length, which implies the
fulfilment of a scaling law analogous to those found in the thermodynamics of
critical phenomena. As a by-product, we find a possible model-free explanation
for the origin of Zipf's law, which should arise as a mixture of conditional
frequency distributions governed by the crossover length-dependent frequency.
