Tutorials on key (univariate) probability distributions used in statistical analysis. For a description of multivariate distributions see Multivariate Statistics.
Topics
- Normal Distribution
- Sampling Distributions
- Binomial and Related Distributions
- Student’s t Distribution
- Chi-square and F Distributions
- Other Key Distributions
- Distribution Fitting
- Order Statistics
- Testing for Normality and Symmetry
References
Wikipedia (2020) List of probability distributions
https://en.wikipedia.org/wiki/List_of_probability_distributions
Hastings, N., Peacock, B. (2011) Statistical distributions. 4th Ed, Wiley
https://www.wiley.com/en-us/Statistical+Distributions%2C+4th+Edition-p-9780470390634
Hi Charles,
Does your package offer functionality for the choice of bandwidth; specifically, I am interested in the Sheater Jones approach. Alternatively, can it be programmed into excel VBA?
Martyn
Hi Martyn,
I am sorry, but the software package doesn’t provide Sheater Jones support. I am sure that it can be programmed used Excel VBA.
Charles
I have an question that is related to distributions but is the inverse of the usual fitting of a set of discrete values to a distribution curve. Is there a method to get a formula for a curve that matches a kind of normal distribution given a specific mean, median, and mode? The closest thing I have found is a “skew normal distribution” that takes the mean and median as input but not the mode. I can mentally “see” how such a curve would look but haven’t found any formulas that describe it. It also seems like the standard deviation would be needed but I’m not sure if that really applies to a skewed distribution. Also, we wouldn’t have to worry about multiple peaks – just the single mode.
Hello Charles,
The mean, mode and median should all be equal to the same value when you have a normal distribution. None of these parameters is useful in obtaining the standard deviation, which is essential to estimating the specific normal distribution.
From your discussion about a skewed distribution, perhaps you are interested in fitting the data, based on the mean, median and mode, to a non-normal distribution. If you pick a specific distribution you can use the formulas for the mean, median and mode (based on the parameters that characterize that distribution) and solve for the parameters of that distribution (if there is a unique solution). If you need to select between two or more distributions you can choose the one with the smallest AIC value.
Charles
Hello. Your add-in is great, much appreciate all the work and providing it for free.
I don’t know that much about statistics or probability. Linked pic is from a stock-charting program and is a histogram of the distribution of a 10 period correlation between two markets over a period of time. If I import this data into Excel, I’d like to see what percentage is at various levels, for instance above .80, below 0 etc. I’m interested in finding the probability that when it reaches a certain level, like -.40 for instance, that it will reverse. Would any of your components help me with this and if so, which ones? Thanks much.
https://www.dropbox.com/s/fyaqq0dp9xg4mtg/10%20Corr%20Distribution.jpg?dl=0
Hello Harold,
Thanks for your positive comment about the Real Statistics add-in.
If you have the data used to create the histogram, then you can do what you are asking for. See the webpage
https://real-statistics.com/probability-functions/discrete-probability-distributions/
Charles
I have a data for which I am trying to determine the probability distribution that best fits it. Would this add-in help me with this?
Alex,
Yes. This capability was just added to the Real Statistics add-in.
Charles
Looking for excel based worksheet to attend some of the statical solutions
You can download the examples shown on the website (for free) from the webpage
Examples Workbooks
Charles