Randomly generated lyrics using mixture models: the poem that Frank Sinatra never sang

In this article, we use a simple method to generate words from a pool of several songs. The approach is based on fitting a finite mixture of geometric probability mass functions to the distribution of the frequencies of the words as they occur in the pool. The classification of the lyrics with the estimated probabilities of belonging to each of the class yields a way of generating a given number words. This statistical procedure can be complemented with human composition of a poem using the generated lyrics. An application with 63 songs of Frank Sinatra illustrates how the methodology was used to compose the new poem Young.