PMID- 17994942
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20080103
LR  - 20071112
IS  - 1539-3755 (Print)
IS  - 1539-3755 (Linking)
VI  - 76
IP  - 4 Pt 1
DP  - 2007 Oct
TI  - Estimator of a non-Gaussian parameter in multiplicative log-normal models.
PG  - 041113
AB  - We study non-Gaussian probability density functions (PDF's) of multiplicative 
      log-normal models in which the multiplication of Gaussian and log-normally 
      distributed random variables is considered. To describe the PDF of the velocity 
      difference between two points in fully developed turbulent flows, the 
      non-Gaussian PDF model was originally introduced by Castaing [Physica D 46, 177 
      (1990)]. In practical applications, an experimental PDF is approximated with 
      Castaing's model by tuning a single non-Gaussian parameter, which corresponds to 
      the logarithmic variance of the log-normally distributed variable in the model. 
      In this paper, we propose an estimator of the non-Gaussian parameter based on the 
      q th order absolute moments. To test the estimator, we introduce two types of 
      stochastic processes within the framework of the multiplicative log-normal model. 
      One is a sequence of independent and identically distributed random variables. 
      The other is a log-normal cascade-type multiplicative process. By analyzing the 
      numerically generated time series, we demonstrate that the estimator can reliably 
      determine the theoretical value of the non-Gaussian parameter. Scale dependence 
      of the non-Gaussian parameter in multiplicative log-normal models is also 
      studied, both analytically and numerically. As an application of the estimator, 
      we demonstrate that non-Gaussian PDF's observed in the S&P500 index fluctuations 
      are well described by the multiplicative log-normal model.
FAU - Kiyono, Ken
AU  - Kiyono K
AD  - College of Engineering, Nihon University, 1 Naka-gawara, Tokusada, Tamura-machi, 
      Koriyama City, Fukushima 963-8642, Japan.
FAU - Struzik, Zbigniew R
AU  - Struzik ZR
FAU - Yamamoto, Yoshiharu
AU  - Yamamoto Y
LA  - eng
PT  - Journal Article
DEP - 20071008
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
EDAT- 2007/11/13 09:00
MHDA- 2007/11/13 09:01
CRDT- 2007/11/13 09:00
PHST- 2007/05/29 00:00 [received]
PHST- 2007/08/16 00:00 [revised]
PHST- 2007/11/13 09:00 [pubmed]
PHST- 2007/11/13 09:01 [medline]
PHST- 2007/11/13 09:00 [entrez]
AID - 10.1103/PhysRevE.76.041113 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 1):041113. doi: 
      10.1103/PhysRevE.76.041113. Epub 2007 Oct 8.