<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.</p>
</abstract>

The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.

Labels distance in bucket recursive trees with variable capacities of buckets

Department of Statistics, Science and Research Branch

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Labels distance in bucket recursive trees with variable capacities of buckets"}

The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and...

Labels distance in bucket recursive trees with variable capacities of buckets

Published Online: Dec 30, 2021

Page range: 413 - 426

DOI: https://doi.org/10.2478/ausm-2021-0025

Keywords
bucket recursive trees, trivariate generating function, partial differential equations, depth, distance

© 2021 S. Naderi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Labels distance in bucket recursive trees with variable capacities of buckets

Published Online: Dec 30, 2021

Page range: 413 - 426

DOI: https://doi.org/10.2478/ausm-2021-0025

Keywordsbucket recursive trees, trivariate generating function, partial differential equations, depth, distance

© 2021 S. Naderi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
bucket recursive trees, trivariate generating function, partial differential equations, depth, distance