Volume 15, Issue 5
The Lognormal Distribution and Quantum Monte Carlo Data

Mervlyn Moodley

Commun. Comput. Phys., 15 (2014), pp. 1352-1367.

Published online: 2014-05

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  • Abstract

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method entails reconstructing the probability distribution of a set of data, with given mean and variance, that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation. In doing so, we perform a numerical evaluation of the renormalized sum of lognormal random variables. This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

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@Article{CiCP-15-1352, author = {}, title = {The Lognormal Distribution and Quantum Monte Carlo Data}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1352--1367}, abstract = {

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method entails reconstructing the probability distribution of a set of data, with given mean and variance, that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation. In doing so, we perform a numerical evaluation of the renormalized sum of lognormal random variables. This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190313.171013a}, url = {http://global-sci.org/intro/article_detail/cicp/7141.html} }
TY - JOUR T1 - The Lognormal Distribution and Quantum Monte Carlo Data JO - Communications in Computational Physics VL - 5 SP - 1352 EP - 1367 PY - 2014 DA - 2014/05 SN - 15 DO - http://doi.org/10.4208/cicp.190313.171013a UR - https://global-sci.org/intro/article_detail/cicp/7141.html KW - AB -

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method entails reconstructing the probability distribution of a set of data, with given mean and variance, that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation. In doing so, we perform a numerical evaluation of the renormalized sum of lognormal random variables. This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

Mervlyn Moodley. (2020). The Lognormal Distribution and Quantum Monte Carlo Data. Communications in Computational Physics. 15 (5). 1352-1367. doi:10.4208/cicp.190313.171013a
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