Skew Normal Distribution

[nicedanmonkey]

I am trying to turn a formula for a skew normal distribution into an actual excel formula but am having trouble. I'm not sure how to implement integrals in excel. Here is a link to the formula and to the wikipedia article.

Formula: http://upload.wikimedia.org/math/6/2/8/628a96d51ba225eee1157849e8c52c9b.png
Wiki Article: http://en.wikipedia.org/wiki/Skew_normal_distribution

Basically I am going to have a series of X values in column A. In column B I will have the Skew Normal Distribution formula to give me a value for each X value.

I completed a similar spreadsheet with a Normal Distribution Formula

Formula: http://upload.wikimedia.org/math/e/9/9/e995ab18aed54262088171e9e8fc0d8b.png
Wiki Article: http://en.wikipedia.org/wiki/Normal_distribution

This is the excel formula I used
=((1/(SQRT(2*PI()*$I$1))*EXP(-((A2-$I$2)^2)/2*$I$1)))
I1 is the Variance and I2 is the Mean. A2 is the X value.

 

[joeu2004]

[.... deleted by me ....]

 

[kalak]

I haven't done much stats for a few years, but last work was investigating the Double Pareto distribution, which may be of some interest to you.

Look it up on Google if interested.

The stuff I did is buried in an old hard drive in the archives somewhere, so I can't offer much more info.

 

[DaveM123456789]

Alright, I'm just gonna go ahead and paste the data. Let me know if there's anything else I can add to help!

Thanks everyone.
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[DaveM123456789]

Here's a little more info on what my issue is specifically. I've forecasted the number of job bookings my company will receive every month. I want to then distribute each month's forecasted bookings over the months the jobs themselves will happen (So, a table with month of booking on the x axis, month of job on the y axis). To do that, I'm using this normal distribution curve. But, about 2% goes negative. So, my distribution every month is only accounting for 98% of the total forecasted bookings for that month. Over the course of the year, that 2% adds up to a big discrepancy in total projected sales!

Here's an image of the heat map https://drive.google.com/open?id=0B4YBXwQLOLoYQWM0ZldTSHNER2c (The other factor in the heat map is that our work is seasonal, so along the bottom is the variance to the mean for each month, that variance is factored in, to make sure our monthly projections are properly weighted.)

And here's an image of the normal distribution curve, vs the historical percentile distribution https://drive.google.com/open?id=0B4YBXwQLOLoYTE1QblpOZno2TXM

 

[shg]

This is at the furthest reach of my ability to pretend I know anything about statistics ...

I thought a log-normal distribution sounded appropriate, but you're right, it's a terrible fit.

And skew-normal happily allows negative values.

What looks closer, though not great, is a beta distribution with alpha ~ 2.2 and beta ~ 4.7.

I don't think I can offer any value to this, sorry.

 

[DaveM123456789]

Thanks for trying at least!

How did you calculate the alpha and beta?

 

[shg]

I used Solver to match the PDF of your data and the beta distribution.

 

[DaveM123456789]

Thanks!

 

[shg]

You're welcome.

 

[Smora]

Hey shg,

Would you happen to know if there would be an inverse formulation in Excel for this formula? I am trying to use it for price trends, where I want to represent a bit the distribution around a price point but reflecting in some portion the trend of the curve.

Thanks
S

Maybe like this:



=2/w * NORMDIST((x-e)/w, 0, 1, FALSE) * NORMSDIST(a*(x-e)/w)