A discrete distribution (see discrete random variable) with one parameter θ (0<θ<1), for whichwhere ln is the natural logarithm. The distribution has mean and variance equal torespectively. A simple recurrence relation links successive probabilitiesThe distribution is much in use in the context of species diversity. If, when sampling a mixed-species population, n species occur just once, then it is commonly found that, for some θ, the numbers of species occurring twice, thrice,…are approximately ½nθ, ⅓nθ²,…. The ratio n/θ is the index of diversity. The distribution is also suitable for modelling the numbers of items of a product bought by a buyer in a given time period.