The solar wind is a driven nonlinear, nonequilibrium system with large jumps and fluctuations in the temporal profiles of the magnetic field strength B. Relatively large clusters of strong fields (“merged interaction regions,” MIRs) form beyond 1 AU, grow out to ≈5–30 AU, and decay slowly between ≈30 AU and at least 90 AU. We analyze the probability distribution functions (PDFs) of fluctuations of B observed by Voyager 1 between 7 and 87 AU on scales from 1 to 128 days during each of four years (1980, 1991, 2001, and 2002). The 32 PDFs of the increments of B can be described by a single function, the q-exponential distribution of the nonextensive Tsallis statistical mechanics. The tails of the PDFs are described by the entropic index q, which is scale dependent. The Tsallis distribution has a finite variance when q < 5/3 and a divergent moment when q ≥ 5/3. For the 1980 and 1991 data (near 8 and 45 AU, respectively), q ≥ 5/3 at all scales, owing to large tails of the PDFs caused by large fluctuations and jumps in B(t). For the 2001 and 2002 data (between 80 and 87 AU), q < 5/3, and q approaches 1 (the PDF tends to a Gaussian) at large scales. The standard deviation and kurtosis of the observed increments of B vary with the scale of the fluctuations. The transition from q > 5/3 at <45 AU to q < 5/3 at >80 AU suggests the possibility of a phase transition in the distant heliosphere.