[Scilab-users] advice on a pseudo-"bandwidth" calculation

[Tim Wescott]

On Tue, 2015-06-09 at 14:36 +0000, Carrico, Paul wrote:
> Dear all
> 
>  
> 
> I’m currently thinking  in a way to compare experimental have a bell
> shape, composed of points and not connected to any parametric curve
> (the bell shape assumption could answer to the need in a first step).
> 
>  
> 
> A way I can imagine is to calculate a kind of “ bandwidth” (-3 db).
> 
>  
> 
> I add a look in the Scilab help but nothing obvious appears
> 
>  
> 
> what is the best way to proceed to:
> 
> - calculate/determine the intersection points with the
> “pseudo”-curves,
> 
> - the number of points may change and may have different abscissa ?
> 
> - the points could not necessarily by expressed by a parametric curve
> (to fit on before calculating the intersection),
> 
>  
> 
> Any suggestion are welcome
> 
>  
> 
>  
> 
> NB: please find hereafter a basic example using a gauss curve (just to
> illustrate the purpose)
> 
To the extent that you can do so without giving away any proprietary
information, could you please tell us what you're really trying to do?

Citing a Gaussian distribution (a "bell curve") implies that you're
trying to find a probability density, but citing a "bandwidth" implies
that you're trying to characterize some sort of a signal processing
system.  Those two concepts don't exactly fit well together when you're
talking of one set of data.

If you're taking a bunch of measurements and you're assuming a Gaussian
distribution of errors, and you want to estimate the mean and variance
of the distribution, then you want to use mean(x) and var(x).  This is
kind of the quick & dirty way to do things, but with a large enough
sample it's not going to be very far off the mark (if you have less than
a couple of dozen samples you may want to investigate the Student t
distribution, but I don't like recommending it if you don't have a solid
background in statistics).

-- 

Tim Wescott
www.wescottdesign.com
Control & Communications systems, circuit & software design.
Phone: 503.631.7815
Cell:  503.349.8432