Quote from: 375CT on June 27, 2014, 08:36:48 AM
Makes sense, but how to be sure? I get and agree to the point you made, but making no sense, well, that's the hard part out of this, because we are not dealing with any way to test the actual implementation.

Litz speaks about standard deviations when he mentions distribution factors. This alone tells us that probability distribution can't be flat. Another proof is that litz's tool gives approx. same results as mine. And mine is based on normal distributions.

Quote from: 375CT on June 27, 2014, 08:36:48 AM
I understand you are recomending going CEP for a more realistic simulation, am I right on my assumption?

No, I'm only recommending CEP for group size measuring. For wez tool you can use monte carlo or CEP depending which properties you value. I decided to go with CEP because for me it was more important to compare different calibers, bullets and conditions than get absolutely accurate results in hitting probability. Problem with monte carlo is that you get slightly different results for every calculation. That's not desirable if you try to compare something.

In practise you can never accurately calculate hitting probability anyway. That's simply because you don't know exact standard daviations for distribution factors. WEZ tool is always at it's best for comparing not for absolute probabilities.

Quote from: mman on June 27, 2014, 06:20:11 AM

Quote from: 375CT on June 26, 2014, 11:44:10 PM
Well, so far the original questions remains, is Litz's WEZ (a term taken from Air Combat for budget error analysis) flat or not?

That's easy one. It must be normal distribution. No sense to use flat distribution, that would lead to strange results.

Makes sense, but how to be sure? I get and agree to the point you made, but making no sense, well, that's the hard part out of this, because we are not dealing with any way to test the actual implementation.

http://ballistipedia.com/index.php?title=Main_Page

Useful link for further discussion.

I understand you are recomending going CEP for a more realistic simulation, am I right on my assumption?

Quote from: 375CT on June 26, 2014, 11:44:10 PM
Well, so far the original questions remains, is Litz's WEZ (a term taken from Air Combat for budget error analysis) flat or not?

That's easy one. It must be normal distribution. No sense to use flat distribution, that would lead to strange results.

Confirmed here

http://msdn.microsoft.com/en-us/library/2dx6wyd4(v=vs.110).aspx

Random in VB.net yields an uniform distribution...now, I need to figure out how bad this could be for creating something akin a WEZ run.

Anyway, like Robert pointed out, a RNG can be easily programmed if such need ever arises with for instance the Ziggurat algorithm.

Mman, thanks for the links, they just confirmed my suspicions on this too.

Now will also review CEP. Well, so far the original questions remains, is Litz's WEZ (a term taken from Air Combat for budget error analysis) flat or not?

http://office.microsoft.com/en-gb/excel-help/rand-function-HP010342816.aspx
This is flat. You can convert it into gaussian if you want.

There is discussion about it:
http://elsmar.com/Forums/showthread.php?t=22358

There seems to be an agreement what robert said about it. It would be interesting to hear why and how bad rand() actually is.

Quote from: admin on June 25, 2014, 01:47:55 PM
In visual basic and as an Excel function I have published random number generators, two of them generate numbers with a constant probability ("flat").
The other one. =bfx_rang(....) generates numbers according to a gaussian distribution.
The properties of Excels random generators did not suit my purpose.

The "flat" distribution is the basis for generating numbers distributed according to another distribution.
For gaussian distributions efficient algorithms can be googled.

Nevertheless, the more random variables involved in a simulation, the less details of a certain random variable matter.

Understood the last part, but it's not clear why RANDOM in VB is not good enough. I got the point on Gaussian but I read somewhere that random() is indeed gaussian, so more confussion for me at least

What's wrong with excel's RAND ( ) ? My monte carlo is based on that and I got same averages as some references I used...

In visual basic and as an Excel function I have published random number generators, two of them generate numbers with a constant probability ("flat").
The other one. =bfx_rang(....) generates numbers according to a gaussian distribution.
The properties of Excels random generators did not suit my purpose.

The "flat" distribution is the basis for generating numbers distributed according to another distribution.
For gaussian distributions efficient algorithms can be googled.

Nevertheless, the more random variables involved in a simulation, the less details of a certain random variable matter.

I'll let robert answer the programming stuff...

If you look into commercial programs gaussian distribution is the most common for gun accuracy. To apply anything else you would need really extensive testing and fitting.

I have done a shooting diary as well (see Group and velocity statistics thread) and I have now around 500 groups in my database. When it comes to statistics it's not much but it is something. In avarage all the real world group measures I have saved fit very well to gaussian distribution. So I would say it really is pretty good probability distribution for the application.

If you accept that holes distribute according to gaussian distribution you can calculate lot's of things. For example I have done extensive testing with monte carlo comparing different group size measures. There are lots of them. To mention few: radial extreme spread (the most common and worst), ES X and Y directions, radial standard deviation, SD X and Y directions, diagonal, Circular error probability (which is best I have found). There are at least two important things which define the best measure: 1. effectivenes which means that how many rounds you have to shoot for two different loads to define which is more accurate. 2. independence which means how number of shots or group shape affects to measure in question.

The best feature in SD based group measures is that they are not depended on number of shots in the group like extreme spread measures. For example with monte carlo you can calculate that 10-shot group is around 1,6x (if my memory serves me right) larger than 3-shot group. And that's only true if groups are round in average. While CEP is in average approx. the same for both 3- or 10-shot groups.  If group ellipcity factor is not higher than 4.

Quote from: 375CT on June 24, 2014, 07:29:08 AM
Mman, if you don't me asking, why you state your work is not mathematically exact?

Read the article about CEP. Derivation includes few approximations at least on ellipcity and bias. Then again I have assumed that all the dispersion factors are independed. This is pretty good approximation but not exactly true as roberts states on Hit probability thread.

Excellente discussion and insight!

Just a simple question, since I'm not that familiar with Excel programming (just the basics), do you think that using a random number generator (RNG), for using a common programming language, could do the same? I mean, assuming that the RNG is based on a Gaussian distribution?

On the other hand, what other kind of probability distribution do you guys thinks is worth exploring for a realistic scenario?

I find this subject very interesting for developing some sort of BfX simulator, besides the excellent work already done by Robert.

Mman, if you don't me asking, why you state your work is not mathematically exact?