=+6. Let N1,...,Nm be an i.i.d. sample from the Zipf distribution with values n1,...,nm. If at least
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=+6. Let N1,...,Nm be an i.i.d. sample from the Zipf distribution with values n1,...,nm. If at least one ni > 1, then prove that the maximum likelihood estimate of s is uniquely determined by the equation
− d ds ln ζ(s)=Es(ln N) = 1 m
m i=1 ln ni.
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