The above equation is a generalised Cauchy distribution which reduces to a standard Cauchy distribution for C=1 and becomes a Gaussian (normal) distribution as C→∞. The parameter Di controls the width of the distribution (in the Gaussian limit Di=σi is simply the standard deviation) while the global value C controls the size of the tails.
In one example, C is 3/2, which lies between Cauchy and Gaussian, so that the likelihood becomes: