Null distribution: For data which can be negative as well as positive, the null distribution for cosine similarity is the distribution of the dot product of two independent random unit vectors. This distribution has a mean of zero and a variance of formula_32 (where formula_33 is the number of dimensions), and although the distribution is bounded between -1 and +1, as formula_33 grows large the distribution is increasingly well-approximated by the normal distribution. Other types of data such as bitstreams, which only take the values 0 or 1, the null distribution takes a different form and may have a nonzero mean.