# Thread: Help with normal distribution

1. ## Re: Help with normal distribution

Originally Posted by MrDavid
Hi, rogojel, thank you for taking the time and reply

well, I am working with inventory systems with probabilistic demand, so I must work with the probability distribution to obtain the information of the samples (leatime, security inventory, quantity, etc etc).

Since I do not know which statistical distribution the data fit, I used several software. The results of the software show that the data fit a normal distribution, but I must prove it theoretically.

So I need to prove theoretically that these data fit a normal distribution, the problem is that they are more than 3000 samples of discrete data, a normal probability plot for each one is a little inappropriate.

hi,
if I understand you correctly you have many data points but they refer to different groups, so you have a small number of data per group? And you need a model per each group?

There is a saying that a small dataset is always normally distributed, a large one never is - this means that the power of the normality tests is such, that they will pretty much always fail to reject the null for a small dataset. So, running the tests for small groups is not going to help you, except in really extreme cases, as has already been pointed out here. Depending on what you need to do, you might want to consider simply using your data to make predictions (as in boostraping, by creating larger samples by sampling with replacement from your original data). That could give you an idea of how often the demand would exceed a given limit, for example.

regards

2. ## The Following User Says Thank You to rogojel For This Useful Post:

MrDavid (02-06-2017)

3. ## Re: Help with normal distribution

Originally Posted by rogojel
hi,
if I understand you correctly you have many data points but they refer to different groups, so you have a small number of data per group? And you need a model per each group?

There is a saying that a small dataset is always normally distributed, a large one never is - this means that the power of the normality tests is such, that they will pretty much always fail to reject the null for a small dataset. So, running the tests for small groups is not going to help you, except in really extreme cases, as has already been pointed out here. Depending on what you need to do, you might want to consider simply using your data to make predictions (as in boostraping, by creating larger samples by sampling with replacement from your original data). That could give you an idea of how often the demand would exceed a given limit, for example.

regards
I will try to apply these advice, thank you very much for the help

4. ## Re: Help with normal distribution

Originally Posted by ondansetron
Yes, this is why I asked if there was a specific purpose (you just asked it more clearly). I also want to stress that the OP keeps saying he wants to prove the data come from normal distribution (or fit it)-- in those tests, that would be equivalent to saying the null hypothesis is true. This is an incorrect conclusion as we can never prove the null, and failure to reject the null does not count as evidence for the null. So, given this, the OP should be cautious not to interpret the results that he has proven normality in anyway. At best, there would be insufficient evidence of non-normality (but again, doesn't prove or support normality).
Nice posts in this thread, ondansestron - you really seem to be making a positive contribution on the forums

5. ## Re: Help with normal distribution

Originally Posted by CowboyBear
Nice posts in this thread, ondansestron - you really seem to be making a positive contribution on the forums
Thanks! I'm glad to hear that.

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