Multiscale Probability Density Function Analysis
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The programs are given WITHOUT ANY WARRANTY; without even an implied statement of merchantability or fitness for a particular purpose. If you decide to use these programs, you do so entirely AT YOUR OWN RISK.

Usage notes
All programs are called from the command line. Running each program with the option -h also displays a short usage note.


Programs
Binary excutable software for Windows XP/Vista/7 is available.

1. hrv_NGindex.exe
Estimation of non-Gaussianity index from RRI time series (Fig. 1). This program processes the following procedures:
(1) Resampling of RRI time series included in the input file.
(2) Detrending and coarse-graining of the resampled time series.
(3) Estimation of non-Gaussian index at a fixed scale.
(4) Estimation of the probability distribution.

Through those processes, hrv_NGindex.exe genarates 2 files, "***_TS.txt" and "***_PDF.txt", where *** is the name of the input file. In "***_TS.txt" and "***_PDF.txt", you can see the resampled time series and coarse-grained time serimes (Fig. 2), and the estimated PDF and the approximated PDF with the estimated lambda (Fig. 3), respectively. Usage:
hrv_NGindex [Options] rri_data_file > output_file
where "rri_data_file" must have one column data of RRI without header lines.
-d detrending using a polynomial of degree N
-s scale (sec)
-q order of the absolute moment for estimation
-0 Using step step interporation
-3 Using cubic spline interpolation
-1 linear interpolation
-t Resampling time interval, T
-v Standardize
-m fitting algorithm (M=1:normal equationCM=2:SVD)
-h print this usage summary
Usage examples:
hrv_NGindex.exe rri_sample.txt > result.txt

hrv_NGindex.exe -d 3 -s 25 -3 -t 0.25 -q 0.25 rri_sample.txt > result.txt




Fig. 1: Plot of "rri_sample.txt".


Fig. 2: "rri_sample_TS.txt" includes the resampled time series (top) and coarse-grained time series (bottom).



Fig. 3: "rri_sample_PDF.txt" includes the estimated probability density function (circles) at a coarse-grained scale and its approximation using a multiplicative log-normal model (solid lines).

2. xexpy.exe
Generating time series of independent and identically distributed non-Gaussian random variables in a multiplicative log-normal model.
Usage:
xexpy N lambda

3. lmd2stat.exe
Estimation of the non-Gaussian parameter in a multiplicative log-normal model.
Usage:
lmd2stat [Options] file
-m order of the absolute moment
-w coarse-grained level of the time series
-h show a short usage note
Usage example:
xexpy 100000 0.8 > sample.txt
lmd2stat sample.txt


4. lncas.exe
Generating time series of log-normal cascade model.
Usage:
lncas lambda N_{cascade_steps} M

5. msfluc.exe
Generating coarse-grained time series after detrending.
Usage:
msfluc [Options] < file
-d order of detrending
-w coarse-grained level of the time series
-h show a short usage note
Usage example:
lncas 0.8 14 4 > sample.txt
msfluc -d 3 -w 16 < sample.txt > sample16.txt
lmd2stat sample16.txt