import string


def letterDensity(authors):
    """ Calculate the empirical distribution of first letters.
    """
    authors['firstLetter'] = authors.firstLetter.apply(lambda x: x.lower())
    authors = authors[authors['firstLetter'].isin([i for i in string.ascii_lowercase])]
    byLetter = authors.groupby('firstLetter').name.agg('count')
    total = byLetter.sum()

    return byLetter / total