Discover MakerZone

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

Learn more

Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

Apply Today

Thread Subject:
tending to infinity for standard deviation

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 04:38:08

Message: 1 of 15

Hi everyone,

I am doing some coding in Matlab , but have comes across something I am stumbling at.
 Would be grateful for your help.

If ,

  lim x = 0 ; as x tends to infinity

does this also imply,

lim standard_deviation_of_x = 0 ; as x tends to infinity

Your help is appreciated,
cheers
aiden

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 04:47:08

Message: 2 of 15


Please let me rephrase my question :

if x tends to infinity based on some function (where x is a number) ,
does it imply that the standard deviation of x tend to Zero ?

cheers,
aiden

Subject: tending to infinity for standard deviation

From: Matt J

Date: 17 Jul, 2011 12:23:07

Message: 3 of 15

"Aidy" wrote in message <ivtpgc$s3k$1@newscl01ah.mathworks.com>...
>
> Please let me rephrase my question :
>
> if x tends to infinity based on some function (where x is a number) ,
> does it imply that the standard deviation of x tend to Zero ?
================

No. Consider

X_n=[1 2 3] + n

Clearly as n-->infinity, then X_n(i) likewise goes to infinity, for all i. However,

std(X_n)=std([1 2 3]) =1

This is true for all n and therefore std(X_n) --->1 as n-->infinity.

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 13:35:10

Message: 4 of 15

Matt,

How did you derive the statement :

std(X_n)=std([1 2 3]) =1

?

thanks for helping,

aiden

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 13:44:09

Message: 5 of 15

Matt,

Let me rephrase my problem once again :

x is a vector with a standard deviation ,not a number. It is infact a 2D coordinate position.

So, I have :

x = [ 20 ; 34555] +/- 255
where 255 is the standard deviation.

Now,I know that my vector x tends to infinity and I am getting a rather large standard deviation for it, which I think means that there is high uncertainty associated with 'x' (or at least this is what I assume ,not 100% sure on that).

As my vector x tends to positive or negative infinity , the standard deviation increases.

I am tending to believe since I am highly uncertain about the position of my 2D coordinate vector which could be any in the range of negative Infinity to Positive Infinity , this physically means its 2D position is very "uncertain" and thus may also be infinite and may increase as the vector x tends to Inf. So I want to apply a limit rule for the standard deviation of vector x.....

So, can I make the assumption that if x tends to infinity , then its std_x also tends to Infinity and thus I apply a limit, then its std_x will tend to zero OR is it 1?

thanks,
aiden

Subject: tending to infinity for standard deviation

From: Greg Heath

Date: 17 Jul, 2011 13:55:41

Message: 6 of 15

On Jul 17, 12:38 am, "Aidy " <aidenj...@gmail.com> wrote:
> Hi everyone,
>
> I am doing some coding in Matlab , but have comes across something I am stumbling at.
>  Would be grateful for your help.
>
> If ,
>
>   lim   x  = 0 ; as x tends to infinity
>
> does this also imply,
>
> lim   standard_deviation_of_x = 0 ; as x tends to infinity
>
> Your help is appreciated,


Yes. For example:

close all, clear all, clc
N = 1e4 % Make as large as you are patient
for n = 1:N
    x(n,1) = 1/n; % or whatever you want
    meanx(n,1) = mean(x);
    stdx(n,1) = std(x);
end
summary = [x(end) meanx(end) stdx(end)]
figure, hold on
plot(x)
plot(meanx,'r')
plot(stdx,'g')

Hope this helps.

Greg

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 14:08:08

Message: 7 of 15

hi Greg,

please, also refer to the last message I posted on my 2D coordinate vector question and let me know if you think it still applies ? I have explained my full problem in this post.


thanks again,
aiden

Subject: tending to infinity for standard deviation

From: Greg Heath

Date: 17 Jul, 2011 14:19:59

Message: 8 of 15

On Jul 17, 8:23 am, "Matt J " <mattjacREM...@THISieee.spam> wrote:
> "Aidy" wrote in message <ivtpgc$s3...@newscl01ah.mathworks.com>...
>
> > Please let me rephrase my question :
>
> > if x tends to infinity based on some function (where x is a number) ,
> > does it imply that the standard deviation of x tend to Zero ?
>
> ================
>
> No. Consider
>
> X_n=[1 2 3] + n
>
> Clearly as n-->infinity, then X_n(i)  likewise goes to infinity, for all i. However,
>
> std(X_n)=std([1 2 3]) =1
>
> This is true for all n and therefore std(X_n) --->1 as n-->infinity.

I think the OP was considering the running stdv of a 1-D
time series.

In which case the answer must be Yes:

As x(n)--> inf,

meanx(n) = mean(x(1:n)) --> inf

and for any fixed point x(m),

abs(x(m)-meanx(n)) --> inf

For example,

close all, clear all, clc
N = 1e4 % or larger if you want
for n = 1:N
    x(n,1) = n; % or whatever you want
    meanx(n,1) = mean(x);
    stdx(n,1) = std(x);
end
summary = [x(end) meanx(end) stdx(end)]
figure, hold on
plot(x)
plot(meanx,'r')
plot(stdx,'g')

Hope this helps.

Greg

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 14:36:08

Message: 9 of 15

hi Greg,

please, refer to the l message 5 of 8. I have explained my full problem in this post.

I posted on my 2D coordinate vector question and let me know what you think,please ?

cheers,
aiden

Subject: tending to infinity for standard deviation

From: Matt J

Date: 17 Jul, 2011 15:20:09

Message: 10 of 15

"Aidy" wrote in message <ivuov9$e2t$1@newscl01ah.mathworks.com>...
> Matt,
>
> Let me rephrase my problem once again :
>
> x is a vector with a standard deviation ,not a number. It is infact a 2D coordinate position.
>
> So, I have :
>
> x = [ 20 ; 34555] +/- 255
> where 255 is the standard deviation.
=====================

Aidy, your question is simply unanswerable until you clarify what in your problem is deterministic, what is stochastic, and how x "tends to infinity". In what you've stated above, x appears to be a random vector with a fixed mean of
[ 20 ; 34555]
and whose components have a fixed standard deviation of 255. It is therefore impossible to understand how the standard deviation could be tending asymptotically to anything but the constant value fo 255 that you've stated.

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 15:47:07

Message: 11 of 15

Hi matt,

basically, I have a function that defines the vector x.
Now this function produces a vector x which is valid from [0 , 0] to [Inf_x, Inf_y].

I have realized that from my function, I can get different vectors as my answer. Now as my x_coord and y_coord of my 2D vector increases , I also see a trend where generally the standard deviation will also increase.

So can I assume that , whatever my value my 2D vector is ,its standard deviation tends to Infinity ?

And as a result, I how somehow impose a limiting rule such that, if I know this Std dev tends to Inf , then it is perhaps 0?

I hope I explained slightly better. thanks again

cheers
Aiden

Subject: tending to infinity for standard deviation

From: Aidy

Date: 17 Jul, 2011 15:51:08

Message: 12 of 15

typo correction*

And as a result, can I somehow impose a limiting rule such that, if I know this Std dev tends to Inf , then it is perhaps 0?

-aiden

Subject: tending to infinity for standard deviation

From: Matt J

Date: 17 Jul, 2011 16:07:08

Message: 13 of 15

"Aidy" wrote in message <ivv05r$1of$1@newscl01ah.mathworks.com>...
> Hi matt,
>
> basically, I have a function that defines the vector x.
> Now this function produces a vector x which is valid from [0 , 0] to [Inf_x, Inf_y].
>
> I have realized that from my function, I can get different vectors as my answer. > I have realized that from my function, I can get different vectors as my answer. Now as my x_coord and y_coord of my 2D vector increases , I also see a trend where generally the standard deviation will also increase.
=========================

But what do x_coord and y_coord signify? Are they the statistical means
of x(1) and x(2)?

The standard deviation of a series of random vectors can behave independently of its mean. There is no way you can draw conclusions about the behavior of the standard deviations from the behavior of their means.

For example, in this series

   x(t)=[3,2]*t +randn(1,2)*t

The mean of x(t) is [3*t,2*t] and therefore it goes to infinity as t--->infinity.
The standard deviation is [t,t] and so it also goes to infinity as t--->infinity

Conversely, this time series

      x(t)=[3,2]*t +randn(1,2)/t


has mean [3*t,2*t] going to infinity, but the standard
deviation [1/t, 1/t] goes to 0.

Subject: tending to infinity for standard deviation

From: Aidy

Date: 18 Jul, 2011 06:05:10

Message: 14 of 15

hello matt,

I will ask something more straightforward.

If x---> Inf
is it correct to imply Std_dev_of_x ----> Inf ?

cheers

Subject: tending to infinity for standard deviation

From: Matt J

Date: 18 Jul, 2011 12:52:08

Message: 15 of 15

"Aidy" wrote in message <j00iel$3in$1@newscl01ah.mathworks.com>...
> hello matt,
>
> I will ask something more straightforward.
>
> If x---> Inf
> is it correct to imply Std_dev_of_x ----> Inf ?
==================

Nope. Here's a counter-example:

 x=1:n; %Goes to infinity

 Std_dev_of_x =arrayfun(@std,x); %is always zero

Here x is a sequence that goes to Inf with increasing n but Std_dev_of_x is zero for all n and so it converges to 0.

Tags for this Thread

What are tags?

A tag is like a keyword or category label associated with each thread. Tags make it easier for you to find threads of interest.

Anyone can tag a thread. Tags are public and visible to everyone.

Contact us