Non-Normal Distribution vs. Gamma Distribution

[fed-up]

Hi Guys,

If I have two distributions. These being the Non-Normal and Gamma Distribution. And if both of them have n.s. KS p value. Then why is the gamma distribution chosen over the Non-Normal Distribution.

All I know is that as a rule of thumb that Non-Normal Distribution is chosen as a last resort. But why is that?

Thanks

[Coury Ferguson]

Does anyone have ideas about this?

[Miner]

The question is unclear. There is no distribution called the "Non-normal distribution". The gamma distribution is one type of many non-normal distributions such as the weibull, exponential, log-normal, uniform, etc. distributions.

In other words, ALL distributions other than the NORMAL distribution is a non-normal distribution.

[fed-up]

In Reply to Parent Post by Miner

The question is unclear. There is no distribution called the "Non-normal distribution". The gamma distribution is one type of many non-normal distributions such as the weibull, exponential, log-normal, uniform, etc. distributions.

In other words, ALL distributions other than the NORMAL distribution is a non-normal distribution.

Hi Miner,
Actually I was using the statistica software, and in there it gives you a list of all the distribution that is fit for your data. and one of the option is called Non-Normal (skewness, Kurtosis). So I am not sure what Non-Normal distribution this is refering to. Because what you said makes sense.
So I have attached the photo for the dialogue box.

Thanks

[Miner]

I briefly checked the Statistica website for the "non-normal distribution".

Statistica appears to be using the family of Johnson and Pearson curves to fit a skewed or kurtotic distribution that does not fit the typical distributions and are arbitrarily calling it the "Non-normal distribution". n.s. appears to mean Not Significant, which would mean that it fits both distributions.

I could not find Statistica's rationale for using Non-normal as a last resort. I am a Minitab user, which offers non-normal capability analysis using a wide variety of distributions as well as the Johnson and Box-Cox transformations of the data into Normal distributions for standard capability analysis. I am speculating that Statistica's Non-normal distribution is their equivalent to these transformations.

One reason that I prefer using Minitab's non-normal analysis over the transformations is that you can compare your data directly to the specifications. When you transform data, you also must transform the specification. This makes it difficult to make direct comparisons between them or explain them to non-statistical people.

[Darius]

Miner

I want also to add about why normal (gaussian) over "non-normal" that

1- Almost all statistics are gaussian based, so as Miner said, transformation is needed unless you use non-parametrical capability indexes.

2- Most of the people think that "non-normal" (non gaussian) is waky behabiur, so something wrong is happening.

3- Most of the people think that if you add enought information, your distribution will be "normal" (another lie to the bucket), based on central limit (good tool, wrong application, specially time based measures tend to be non gaussian because is easer to have delays than to do the things faster).

[bobdoering]

In Reply to Parent Post by Darius

3- Most of the people think that if you add enought information, your distribution will be "normal" (another lie to the bucket), based on central limit (good tool, wrong application, specially time based measures tend to be non gaussian because is easer to have delays than to do the things faster).

True - and the central limit theorm also does not apply to dependent distributions - such as tool wear. Does not matter how much data you have - unless you have a lot of measurement error, and the more measurements you have the more the error becomes the distribution (because measurement error - not to be confused with gage error - is typically normal).

[Bev D]

In Reply to Parent Post by bobdoering

...and the central limit theorm also does not apply to dependent distributions - such as tool wear.

Perhaps a minor point of clarification would be helpful here.
The Central Limit theorem applies for "identically distributed, independent random variables". In practice this means that if we sample RANDOMLY from any distribution, the average of the subgroups will be roughly Normal - close enough that the Normal distribution has analytical value.

And the theorem holds very well to emperical studies: randomly deal from a deck of cards - a perfect uniform distribution - and you will get subgroup averages that are Normally distributed.

In practice (for SPC specifically and for some experiments) we don't have a Random OUTPUT. That is a de facto violation of the conditions required for the central limit theorem. And we do SPC sampling by time series sampling as the process produces product and that stream isn't random. (this is what is meant when Bob refers to a dependent process) When the largest component of variation is piece to piece in a process we do have a random output in time series and this situation was very common in Shewhart's day. It's not uncommon today, but it isn't the majority either.

For capability studies we are dealing with individual values not subgroup averages and in this case the central limit theorom doesn't apply either (obviously as it only applies to subgroup averages). Native distributions (of individual values) are rarely Normal.