2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 343352
author:  Charlotte Brennan and Arnold Knopfmacher 

title: 
The distribution of ascents of size
d
or more in samples of geometric random variables

keywords:  geometric random variables, distributions, generating functions 
abstract: 
We consider words or strings of characters
a
of length
1
a
2
a
3
⋯a
n
n
, where the letters
a
are independently generated with a geometric
probability
i
∈ℤ
ℙ{X=k}=pq
where
k1
p+q=1.
Let
d
be a fixed nonnegative integer. We say that we have
an ascent of size
d
or more if
a
. We determine the mean, variance and limiting
distribution of the number of ascents of size
i+1
≥a
i
+d
d
or more in a random geometrically distributed word.

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reference: 
Charlotte Brennan and Arnold Knopfmacher (2005), The
distribution of ascents of size
d
or more in samples of geometric random variables, in
2005 International Conference on Analysis of
Algorithms, Conrado Martínez (ed.),
Discrete Mathematics and Theoretical Computer Science
Proceedings AD, pp. 343352

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