LeoStatistic
software for data presentation, statistical analysis, marketing and prediction.

Free download:
LeoStatistic.zip or
LeoStatistic.exe
(selfextracting winzip file)


Registration

  • Introduction
  • Data
  • Statistics
  • Results presentation
  • Samples
  • Popular statistics and data analysis
  • X-ray curve.

    Anybody from science community could have old archives with results of experiments made long time ago. Sometimes only in a form of photo or drawing. LeoStatistic can help to transform them into numerical presentation and analyze with most convenience.

    Let's check an example of such task Honestly speaking I did it only for the demonstration sake here, there is no real value in the old X-ray curve of primary stage crystallization of silicate glass... But let's imaging that it has.

    I put the photo in the scanner. Result JPG image is like this (25% of real image size)

    Old X-ray

    Next step was improving the quality of the picture and as very first step to make it mirror like. I used my software LeoPicture.

    Here is a result of enchanting this image (25% of size too):

    Fixed X-ray picture

     

    Now the time to extract data from it. Open LeoStatistic. Click on "Add"  button. Chose "Image". In dialog box click on "From file" then put rectangle of matching physical and virtual coordinates; rectangle isolating the curve, click of "Line" button and get a picture like this:

    Import X-ray data picture
     

    Press button "OK" and data will be transferred in LeoStatistic as a series of two parameters. After editing names of them to "f" for argument, "I" for value and set a size of the mark "1" the screenshot of LeoStatistic will looks like this:

    X-ray data in LeoStatistic

    Two point with argument f near "14" are obviously mistakenly defined. Click at "Show data" it and delete them. Then try the obviously most suitable statistical scheme - "peaks revealing". Small experimentations shows that setting as shown on the screen gives the best results:

    Found peaks in X-ray

    Content of result panel after copy/paste procedure is shown here:

    Function of one argument.	
    Peaks	
    Series 1 (1141 records)	
    y=F(x)	
    Base line: 65.4166*x^2 -200.498*x +215.779 	
    20 peaks found:	
    Noise level = 0.0582873	
    Sum of gauss like peaks: (0.39894228*A/sigma)*exp(-0.5*((x-Average)/St.Dev.)^2)	
    N	Average St.Dev. A	Max. pos.Max. signal	
    1	13	0.11	9.15574	13.3228	35.935	
    2	8	0.79	39.1623	8.18898	19.7526	
    3	16	0.11	3.79076	15.4646	17.9127	
    4	13	0.1	1.32826	12.9764	4.92022	
    5	12	0.19	1.94017	12.252	4.39944	
    6	16	0.09	0.51576 15.8425	3.55087	
    7	9.6	0.095	1.55564	9.6378	3.48018	
    8	15	0.98	6.41223	14.9606	3.42095	
    9	11	0.098	0.64964	11.0866	2.78035	
    10	19	0.43	2.26113	18.8976	2.43301	
    11	18	0.096	0.47355	17.7323	1.85566	
    12	10	0.089	0.46372	9.95276	1.70165	
    13	22	0.11	0.36419	21.8268	1.45019	
    14	21	0.15	0.48002	21.3543	1.31604	
    15	20	0.068	0.15492	20.252	0.996557	
    16	21	0.16	0.19065	20.6929	0.62381	
    17	17	0.11	0.13997	17.1024	0.527019	
    18	18	0.053	0.10091	17.9843	0.46624	
    19	9.2	0.13	0.30741	9.25984	0.411342	
    20	11	0.089	0.01958	10.8031	0.372078

    In the spite the result is already quite satisfactory there is no limits to perfection.

    The original algorithm of finding base line in peaks revealing algorithm is working quite well but its has its limitations... Let's extract a base line from the curve using other tools of LeoStatistic and will apply a peaks revealing algorithm again. 

    Do following steps:

    • Click on ">>" button to return to main panel of "Statistics".
    • Click on "Constructor style" button. In the appeared panel check buttons: "ln(y)", "1", "x.", "x^2" ,"x^3", "x^4".
    • Go to "Data" tab and click "Insert" button. Chose there "Current theoretical scheme" name "It" and click "Insert-->".
    • Check parameter  "It" and button "Modify". In appeared dialog put in edit box a formula "I-It" and press "Modify".
    • Make all parameters except "It" inactive. Go to "View" tab and press histogram button. Learn that null level is about 5. Modify "It" again adding 5 by formula "It+5". To be sure modify again deleting all less then zero.
    • Make "x" argument and repeat peak revealing scheme again.

    Here is a result. to my mind it's slightly better.

    Peals in X-ray with base line

    Function of one argument.	
    Peaks	
    Series 1 (1141 records)	
    It=F(f)	
    Base line: 157.58*f^2 -262.86*f +189.521 	
    16 peaks found:	
    Noise level = 0.293242	
    Sum of gauss like peaks: (0.39894228*A/sigma)*exp(-0.5*((f-Average)/St.Dev.)^2)	
    N	Average St.Dev. A	Max. pos.Max. signal	
    1	13	0.11	8.86342	13.3228	34.7512	
    2	16	0.11	3.78989	15.4646	16.6906	
    3	9.6	0.088	1.31456	9.6378	7.78409	
    4	8.7	0.55	5.66353	8.59843	5.67662	
    5	13	0.09	1.14739	12.9764	4.31099	
    6	12	0.18	1.56676	12.252	4.05199	
    7	19	0.57	4.60636	18.8976	3.68998	
    8	11	0.11	0.73141	11.0866	3.15343	
    9	16	0.072	0.60733	15.8425	2.9234	
    10	15	0.26	0.74742	14.9606	1.9812	
    11	21	0.23	0.87839	21.2598	1.9394	
    12	18	0.14	0.64873	17.6063	1.55988	
    13	10	0.074	0.34612	9.95276	1.45527	
    14	21	0.22	0.87367	20.6614	1.43209	
    15	14	0.041	0.08096	13.6378	1.20954	
    16	14	0.16	0.33168	14.2362	1.04749	
    In any case our advise is carefully check any date produced by any program. There is no substitute for common sense and professionalism.
    Screenshots of the LeoStatistic software:
    click on picture to enlarge

    Building histograms
    Building histogram

    Distribution of two variables.
    Distribution of two variables.

    Approximation (constructor style interface).
    Approximation
    (constructor style interface).

    3D view.
    3D view.

    DOW trend.
    DOW trend.

    Signals revealing
    Signals revealing.

    Near neighbors method
    Near neighbors method.

    Harmonic analysis.
    Harmonic analysis.

    Fit with free format formula.
    Fit with free format formula.

    Curve fit of crystal growth rate.
    Curve fit of crystal growth rate.

    Get data from image file.
    Get data from image file.

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