How to skew a normal Distribution?

[dsanz905-disabl]

I have a attached a rather simple MathCAD sheet (V13) with a rnorm distribution plotted. Can someone suggest how I would go about creating a skew distribution over the same range with the peak a approximately in the first third of the graph?

Thank-you in advance

David

[RichardJ]

The easiest approach would probably be to multiply it by a ramp function.

Richard

[ptc-1368288]

On 1/20/2010 3:51:24 PM, dsanz905 wrote:
>I have a attached a rather
>simple MathCAD sheet (V13)
>with a rnorm distribution
>plotted.
> ...
>David
__________________________

Years ago, I have designed an "assymetric normal" for Leslie (PTC).
I can't try because you didn't "Save as" 11 as recommended by two collabs.

jmG

[TomGutman]

You don't skew a normal distribution. You choose a different distribution to start. You should be defining the relevant range based on the underlying model. Depending on other factors, perhaps a Weibull or a beta distribution might fit your needs. But start with your model, and work from there to determine the appropriate distribution.
__________________
� � � � Tom Gutman

[PhilipOakley]

Try some of the wikipedia approximations for other distributions that are skewed (as Tom suggests).



Philip Oakley

[dsanz905-disabl]

I like to thank everyone who has taken the time to post a response to my question. I have created a monte carlo simulation of which I could use some easy way to create a distribution that appears skewed, hence my question.

Richard: I will try using some sort of ramp function to see if I can get what I am looking for.

jmG: I have attached a new file saved as MathCAD 11 (as requested). I thank-you for any help you may be able to provide me.

Tom: I did not use the distributions you suggested as the data created is related to a "shape" argument. The rnorm function creates the data based on a mean value and Standard Deviation. I suppose I could use the Weibull distribution but I will have to covert the values to fall within the range I am looking for.

[TheodoreM.Bones]

The normal distribution may be perturbed with the addition of noise helter-skelter. Then the skewness changes.

[TomGutman]

Yes, skewed distributions typically have a shape parameter, the controls the skewing. The normal distribution can be characterized by just the mean and standard deviation (position and scale parameters) because it is not skewed.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 1/22/2010 1:22:27 PM, dsanz905 wrote:
>I like to thank everyone who
>has taken the time to post a
>response to my question. I
>have created a monte carlo
>simulation of which I could
>use some easy way to create a
>distribution that appears
>skewed, hence my question.
>
>Richard: I will try using some
>sort of ramp function to see
>if I can get what I am looking
>for.
>
>jmG: I have attached a new
>file saved as MathCAD 11 (as
>requested). I thank-you for
>any help you may be able to
>provide me.
>
>Tom: I did not use the
>distributions you suggested as
>the data created is related to
>a "shape" argument. The rnorm
>function creates the data
>based on a mean value and
>Standard Deviation. I suppose
>I could use the Weibull
>distribution but I will have
>to covert the values to fall
>within the range I am looking
>for.
>
______________________________

If you have generated a data set, the matter is to best fit with a model. At this stage it is pure didactic. You should provide the data set that results from real experiments. There are quite a lot of models that have a "skew parameter". What you call skew may not be skew as the books say ! It may just be a distortion of some unknown kind. Your data set appears a near perfect (if not !) Gaussian. At the stage you are, you should provide a data table of many experiments in order to fit all the data collection for conclusive appreciation.

Read more in the attached.

jmG

[ptc-1368288]

... Mathcad 11 includes 17 PDF.
This work sheet exemplifies all of them +++.
The first one "Frechet" has a scale and skew coefficient. You can figure that if you would supply a data set of many experiments or simulated experiments, it would be the first one to try. Not so simple because it's like restarting statistics back to �1.

Hope it helps ?

jmG

[RichardJ]

Take a look at this thread:

http://collab.mathsoft.com/read?113892,17e#113892

Richard

[TheodoreM.Bones]

Using pure imagination to prepare raw data, here are 2 examples of skewed normal probability data.

[ptc-1368288]

Up until now, the data set is awaited from the originator.
Read more about "Extreme values"

http://www.mathwave.com/articles/extreme-value-distributions.html

jmG

[TheodoreM.Bones]

Thasnks, Jean. What a big event to read.

[ptc-1214470]

Here is my take on a worksheet addressing extreme value statistics, done a few years ago. It analyzes rainfall in the Los Angeles area.
Jim S.

[ptc-1368288]

Thanks Jim, saved as typical model.
But isn't true that law is the Gamma distribution ?
Oh ! the visitor is getting served "� la carte".

Jean

[ptc-1214470]

Jean,
I haven't explored the relationship with the Gamma distribution. I got the extreme value model from "Statistical Theory of Extreme Values and Some Practical Applications" by Emil Gumbel, a monograph published by the National Bureau of Standards in 1954 (while I was a sophomore in college). This document does mention many statisticians and models of the day, but I haven't noticed any reference to the Gamma distribution; it may not have even been identified as such in 1954.
Cheers,
Jim S.

[ptc-1368288]

Jim, very interesting:

http://collab.mathsoft.com/~Mathcad2000/read?132703,17

To me, debating statistics is like debating the sex of the angels, even more difficult if they get only sightly pregnant. From the California rainfall you have collected, it would be interesting to bin the data set and check which best fit. I had intention of doing so, but expected some collab would also contribute.

Jean

[TheodoreM.Bones]

The Gumbel formula for the Extreme Value Distribution (extreme minimum type) may be used if large numerical values are scaled down to permit evaluation numerically without overshoot on running an exponential of an exponential function. The formula given here differs in sign of the variable (x) from the NIST site, and skews to the right. .

[ptc-1368288]

Lot of functions have been called "Extreme". All what it means to me is "Extremely illogical". Taking Jim's data set [California rainfall], if you try an histogram, no matter the binning, Gamma looks a good candidate. I haven't tried other functions. The "Extreme logical lie" is that for the layman, you can tell that the probability of high flood or drought is about this or that in a 0...1 probability scale. But you can't tell in advance which year. Anyway, the collab didn't came back. Paul W. would have loved this data set. More gadgets to best estimate the Gamma parameters [MLE], maybe but again : fiction. Determining one "Extreme" vs another one, that would be interesting, but so what: they are parent.

Thanks Theodore for your interest and contribution.

Jean

[TheodoreM.Bones]

Another simple example with more points. Running
the Smoluchowski algorithm on the same data will
partition the data below and above the mean but will not change the relative probabiliy of each point.

[TheodoreM.Bones]

To illustrate more cheerily the difference between the 2 Gumbel Extra Value Distributions, both are presented here on raw data.

[TheodoreM.Bones]

I have done much research on the topic of skewing a normal probability function and I find the 2 Gumbel formulas I gave in my last posting of GUMBEL3 are trustworthy in skewing data about a mean. They are found also on a NIST site, but typographics on it prevent terms from being shown as exponentials of an exponent. Instead they are shown as products.

[TheodoreM.Bones]

Using a Gumbel type skew on normal probability data has the effect of lowering the mean of the data and equalizing the number of data points on both sides, the skewed half and the remaining other side. Thus, if the 2 halves have the same number of points, the binomial coefficient approaches 1 and all points are treated equally and have equal weights.

[TheodoreM.Bones]

A straightforward application of the Gumbel skew of a normal probability function isn�t workable. Perhaps the Gumbel algorithm isn�t exactly correct on arbitrary live data. The Minerr skewed data of it has to be tweaked to make it agree on the unskewed area. No other Forum member has submitted any examples. Nevertheless, some practical benefit in boosting the reliability of outlier points may be had.

[ptc-1368288]

>No other Forum member has submitted any examples.<<br> _______________________

Can't be more right Theodore !

There are quite a few of these "Extreme values" distributions. Easy to try, but it would be waste of pain & prestige whereas the originator hasn't yet offered some data set, especially knowing in advance that many models don't minerr well and so for real project the fit might be manual.

jmG