A lognormal approximation for the collector's problem

The collector's problem has been well-known for many years and is discussed in several texts on probability, for example Feller. Recent interest has focused on generalizations of the problem and, in line with our present objective, approximations to the distribution of the number N of items that must be bought or collected to obtain a complete set of different items (Dawkins; Levin). The lognormal distribution provides a good approximation to the distribution of N, and appropriate parameter values are found by the matching of moments, which has intuitive appeal.