Common distributions with typical uses and canonical link functions

Cosinor assumes a Normal distribution of Variance.  The list below examines types of distributions.

Distribution    Support of distribution      Typical uses                                                                 Link name    
Normal              real:                                Linear-response data                                                      Identity
Exponential        real:                                Exponential-response data, scale parameters                     Inverse
Gamma 
Inverse Gaussian real:                                                                                                                  Inverse squared
Poisson             integer:                           count of occurrences in fixed amount of                            Log
                                                                            time/space
Bernoulli           integer:                           outcome a single yes/no occurrence                                 Logit
Binomial           integer:                           count of # of "yes" occurrences out of N
                                                                            yes/no occurrences
Categorical       integer:                           outcome of single K-way occurrence K-vector
                                                                   of integer: , where exactly one element in the vector has the value 1
Multinomial      K-vector of integer:           count of occurrences of different types (1 .. K) out of N total K-way occurrences

http://en.wikipedia.org/wiki/Generalized_linear_model