File:Law of large numbers.gif
Original file (1,000 × 600 pixels, file size: 21 KB, MIME type: image/gif)
Captions
Captions
Summary
[edit]
| Description |
English: A plot of the average of n simulated independent Bernoulli trials (each taking a value of +/- 1) to show the law of large numbers and the law of the iterated logorithm.
The graphical difficulty here is that we want to show details for very large values of n. If the y-axis were left untransformed, all we could see is that it converges to zero. If we used a log transformation it would be upset with the negative values. So the y is transformed by something that is very close to a log transformation, namely, y^.12. (The .12 looks nice. Other small powers look about the same.) Humans are very good at seeing "straight lines". So if we transform the x-axis to be almost log also we can make the upper and lower envelopes look almost straight. The correct power is -1/2 of the power used for the y axis. So the plot is x^-.06 vs y^.12. These are basically "log(x)" vs "log(y)". But by using these values, the natural square root behaviour now is a straight line. If you have suggestions for improving the image, let me know and I can generate a new one. A detailed view of the right hand most "pixel" is: .gif) |
| Date | |
| Source | Own work |
| Author | Dean P Foster |
[(untransformed, de-transformable, de-transformably{7.28.09; 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019; 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029})
(untransformed, de-transform, de-transforms; de-transformation, de-transforming, de-transformed{6.29.12, 2013, 2014, 2015, 2016, 2017, 2018, 2019; 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029})]
Licensing
[edit]
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:53, 15 May 2009 | | 1,000 × 600 (21 KB) | Dean P Foster (talk | contribs) | Why won't it accept this file??? |
| 11:51, 15 May 2009 |  | 1,000 × 600 (21 KB) | Dean P Foster (talk | contribs) | Reverted to version as of 11:44, 15 May 2009. THis is the correct file | |
| 11:49, 15 May 2009 |  | 1,000 × 600 (21 KB) | Dean P Foster (talk | contribs) | one more time! added sqrt(n) | |
| 11:46, 15 May 2009 |  | 1,000 × 600 (21 KB) | Dean P Foster (talk | contribs) | added sqrt(n) line | |
| 11:45, 15 May 2009 |  | 1,000 × 600 (15 KB) | Dean P Foster (talk | contribs) | oops wrong file | |
| 11:44, 15 May 2009 |  | 1,000 × 600 (21 KB) | Dean P Foster (talk | contribs) | added sqrt(n) line | |
| 19:55, 13 May 2009 |  | 1,000 × 600 (15 KB) | Dean P Foster (talk | contribs) | {{Information |Description={{en|1=A plot of the average of +/-1 bernulli trials to show the law of large numbers and the law of the iterated logorithm. }} |Source=Own work by uploader |Author=Dean P Foster |Date= 2009-05-09 |Permis |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on bg.wikipedia.org
- Usage on en.wikipedia.org
- Usage on es.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on www.wikidata.org
