The number of distinct values in a geometrically distributed sample

Authors:
Margaret Archibald;Arnold Knopfmacher;Helmut Prodinger
Affiliations:
The John Knopfmacher Centre for Applicable Analysis and Number Theory, Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;The John Knopfmacher Centre for Applicable Analysis and Number Theory, Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Department of Mathematics, University of Stellenbosch, Stellenbosch, South Africa
Venue:
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Year:
2006

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Abstract

For words of length n, generated by independent geometric random variables, we consider the average and variance of the number of distinct values (=letters) that occur in the word. We then generalise this to the number of values which occur at least b times in the word.