logarithmic distribution

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A discrete distribution with one parameter θ(0<θ<1), for which , where ln is the natural logarithm. The distribution has mean and variance equal to , respectively. A simple recurrence relation links successive probabilities The 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 ½, 132,…. 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.

Subjects: Probability and Statistics.

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