Conference rusure::math

692.0. "How to do Arithmatic on Distributions?" by GENRAL::HEINTZE () Fri Apr 17 1987 16:06

I want to know how to define binary arithmatic operations a new domain (is that
the correct term?) where a scalar value is actually a  probability
distribution.    The goal is comprehensive error analysis.    I welcome answers
or references. 
    
(1)  What is the optimal way to store a distribution? 
    
I figured what I would do is store the distribution in an array of records
where the second field in the record indicates how far you are from the mean and
the first field gives you the value. 
    
For example, if you had a distribution that looks like this: 
    
    
                          ...
                         .....
                    ................
+---------+---------+---------+---------+---------+---------+---------+
         10        20        30        40        50        60        70
 ..3456789 ..3456789 ..3456789 ..3456789 ..3456789 ..3456789 ..3456789

A scalar value (as opposed to an array of values (ie, distributions)) might
look something like this:

   R :=
    (
       (20,   1), (21,   1),  (22,   1),  (23,   1), (24,   1), (25,   2)
       (26,   3), (27,   3),  (28,   3),  (29,   2), (30,   1), (31,   1)
       (32,   1), (33,   1),  (34,   1),  (35,   1)
    );

 Is there  a better (more efficient) means of storing a distribution curve?

(2)  Suppose I have two distributions, R (which represents the value of
a resister) and V (which represents the value of DC voltage source connected
to the resistor).

How do I find the distribution that represents the current (represented
with the variable "I") where I := V/R ?

In the more general sense, how do I define addition, substraction,
multiplication and division?

(3)  I believe unary operations are trivial, like sin, cos, tan etc.
I just perform that operation on the first field of each record, right?

(4)  What does it mean when they say a resister has a value of 1000 ohms
plus or minus 10 percent?  Does that mean that 100% of the resisters are
with in that range or does it mean 90% of the resistors are within that
range?  How does this number relate to the standard deviation?

(5)  Refering to (2).  Suppose I am short on storage space and my distibutions
are well behaved.  Can I just store the standard deviation?  If so, how
do I do arithmatic on that?



			Thanks


			Sieg
         

    Ah, this one I happen to know from experience
    
>(4)  What does it mean when they say a resister has a value of 1000 ohms
>plus or minus 10 percent?  Does that mean that 100% of the resisters are
>with in that range or does it mean 90% of the resistors are within that
>range?  How does this number relate to the standard deviation?

    I know a lot of you won't belive this, but it means that:

    	A)  100% of the resistors are between +/-10%, and
    	B)  the distibution over this range will be nearly 
    	    uniform (ie. flat).
    
    
    --  Barry

Re .1:

	I agree with (A), but not necessarily with (B), and for two reasons:

	1)	Resistor manufacturing (so I've been told) consists of making
		them, measuring them, and binning them. The binning takes care
		of (A), but if the manufacturing process creates a weird
		distribution of values (for instance, near the limits of the
		process) there could be a considerable slope to the
		distribution within the binning limits, yielding significant
		nonuniformity.

	2)	Since 1% resistors cost more than 10% resistors, there will
		be holes in the distribution wherever the manufacturer
		decides to bin 1% parts instead of 10% parts.

If you are doing error analysis, you might want to assume (in the absence
of better data) that 50% of the parts are +10% and 50% are -10%....

							Richie