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# Probability Distributions Reference Table

Table Description

I have uploaded a reference table that I created with common probability distributions. Although the same formulas and similar descriptions can be obtained on Wikipedia, I find it useful to have the information contained on one table. The table does not have charts that plot probability density or probability mass functions (PDFs and PMFs) or cumulative distribution functions (CDFs). These charts can be found on Wikipedia or plotted with graphing software using the equations on the table. I find it helpful to look at PDF and CDF plots when learning about the distributions. There might be some closed form CDFs, moment generating functions, or other equations that I omitted from the table. Also, some distributions have various formulations. For example, the four distributions defined below are all very similar, and I imagine that each might be referred to as a negative binomial, although certain specifications are more conventional than others.

1. A distribution of the number of failures in a sequence of Bernoulli trials, before a specified number of successes.
2. A distribution of the number of successes in a sequence of Bernoulli trials, before a specified number of failures.
3. A distribution of the number of successes and failures in a sequence of Bernoulli trials, until a specified number of successes.
4. A distribution of the number of successes and failures in a sequence of Bernoulli trials, until a specified number of failures.

In cases where there are multiple ways to define a distribution, I either used the definition that I prefer, or gave multiple formulations of the distribution. I am including a link to both a PDF of the table and an Excel file that has the table and a VBA macro that centers images across a column or multiple columns. Also included is a link to the MathML markup file that was used to generate the equations on the table. Excel’s equation editor was giving me problems, and I did not want to type $\LaTeX$ code manually, so I searched for a what you see is what you get (WYSIWYG) equation editor on the internet. I ended up finding an open source project, Formulator MathML Editor (http://code.google.com/p/formulator-mathml/), which I think is great. After getting started, I also found a $\LaTeX$ editor, LyX (http://www.lyx.org/), which probably would have worked just as well, with the advantage that I’m more familiar with $\LaTeX$ than MathML. I have spotted and corrected a few errors that I made when creating the table (e.g., I originally had the continuous uniform distribution’s variance equal to $\frac{1}{12}\left(b+a\right)^{2}$, which was corrected to $\frac{1}{12}\left(b-a\right)^{2}$), but there still may be some errors. Please let me know if you find any.

## 3 replies on “Probability Distributions Reference Table”

Rafael Ferreirasays:

Thank you very much for the initiative to put online the Distributions Formulas Table. That´s what I find to have always with me in the pocket smartphone.

stevesays:

Thank you so much for sharing this with me and my class. I currently teach higher level high school mathematics for the international baccalaureate program and this table will be very helpful! Just wanted to let you know that your work is appreciated.

Alfonsosays:

Thanks a lot! JUST what I was looking for.