Need some help

[azzza]

THANKYOU guyz! yes, Jim's code was right (it was similar to someone elses)....I somehow missed his reply!
Yes, that was exactly what i was looking for. lastly, how do i find the frequency of heads perhaps?

Marc Schwartz wrote:

On Tue, 2007-10-16 at 11:53 -0700, azzza wrote:
>
>  
> ok, so suppose a coin is tossed 1000 times. Each time head occurs, we win a
> dollar, otherwise we lose a dollar. Let S(n) be our accumulated winnings
> after n tosses. For instance, if the sequence HHHTT occurs in the first five
> tosses, then S(5) = $1.00 wheras if the sequence HTTTT occurs, S(5) =-$3. So
> now, we want to see how many times during the 1000tosses S9n) will go from a
> positive balance to a negative balanc eor the other way around. So for our
> simulation, S(n) is computed by adding one to S(n-1) if a head occurs, and
> subtracting one form S(n-1) if a tail occurs. A change in sign will occur on
> the nth toss in one of two ways: S(n-2)=1, S(n-1)=0 and, S(n)= -1 OR S(n-2)
> = -1, S(n-1)=0 and S(n)=1. This is equivalent to S(n-2)+ S(n-1)+ S(n)=0.
> so now, n is the numbe rof tosses,  S(n) is the number of heads minus the
> number of tails in n tosses and C is the number of times S(n) changes sign.
> so we initialize n=0, S(-1)=0, S(0)=0, and C(0)=0
>
> now we should,
> -generate u, a uniform number, with the increment, n=n+1 ....(our n=1000)
> -if u<1/2, that is tails occur, set S(n)=S(n-1)-1, and also set
> S(n)=S(n-1)+1
> - If S(n) +S(n-1)+S(n-2)=0, then increment C=C+1.
>
> My issue is simulating this in R, where I need to code the number of sign
> changes, the frequency of heads, and to plot S(n) versus n in a line graph.
>
>
> for each coin toss, the number of sign changes could either be a positive
> number, zero, or a negative number.

I believe that Jim had the right approach in his reply here:

  https://stat.ethz.ch/pipermail/r-help/2007-October/143383.html

and Prof. Koenker has given you a reference on the theory:

  https://stat.ethz.ch/pipermail/r-help/2007-October/143385.html

HTH,

Marc

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[jholtman]

sum(toss == 1) /length(toss) # assuming heads == 1

On 10/16/07, azzza <azza.khogaliali@...> wrote:

>
>
> THANKYOU guyz! yes, Jim's code was right (it was similar to someone
> elses)....I somehow missed his reply!
> Yes, that was exactly what i was looking for. lastly, how do i find the
> frequency of heads perhaps?
>
>
>
> Marc Schwartz wrote:
> >
> > On Tue, 2007-10-16 at 11:53 -0700, azzza wrote:
> >>
> >>
> >> ok, so suppose a coin is tossed 1000 times. Each time head occurs, we win
> >> a
> >> dollar, otherwise we lose a dollar. Let S(n) be our accumulated winnings
> >> after n tosses. For instance, if the sequence HHHTT occurs in the first
> >> five
> >> tosses, then S(5) = $1.00 wheras if the sequence HTTTT occurs, S(5) =-$3.
> >> So
> >> now, we want to see how many times during the 1000tosses S9n) will go
> >> from a
> >> positive balance to a negative balanc eor the other way around. So for
> >> our
> >> simulation, S(n) is computed by adding one to S(n-1) if a head occurs,
> >> and
> >> subtracting one form S(n-1) if a tail occurs. A change in sign will occur
> >> on
> >> the nth toss in one of two ways: S(n-2)=1, S(n-1)=0 and, S(n)= -1 OR
> >> S(n-2)
> >> = -1, S(n-1)=0 and S(n)=1. This is equivalent to S(n-2)+ S(n-1)+ S(n)=0.
> >> so now, n is the numbe rof tosses,  S(n) is the number of heads minus the
> >> number of tails in n tosses and C is the number of times S(n) changes
> >> sign.
> >> so we initialize n=0, S(-1)=0, S(0)=0, and C(0)=0
> >>
> >> now we should,
> >> -generate u, a uniform number, with the increment, n=n+1 ....(our n=1000)
> >> -if u<1/2, that is tails occur, set S(n)=S(n-1)-1, and also set
> >> S(n)=S(n-1)+1
> >> - If S(n) +S(n-1)+S(n-2)=0, then increment C=C+1.
> >>
> >> My issue is simulating this in R, where I need to code the number of sign
> >> changes, the frequency of heads, and to plot S(n) versus n in a line
> >> graph.
> >>
> >>
> >> for each coin toss, the number of sign changes could either be a positive
> >> number, zero, or a negative number.
> >
> > I believe that Jim had the right approach in his reply here:
> >
> >   https://stat.ethz.ch/pipermail/r-help/2007-October/143383.html
> >
> > and Prof. Koenker has given you a reference on the theory:
> >
> >   https://stat.ethz.ch/pipermail/r-help/2007-October/143385.html
> >
> > HTH,
> >
> > Marc
> >
> > ______________________________________________
> > R-help@... mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
> >
>
> --
> View this message in context: http://www.nabble.com/Need-some-help-tf4624513.html#a13241118
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
Jim Holtman
Cincinnati, OH
[phone]

What is the problem you are trying to solve?

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[Nordlund, Dan (DSHS/RDA)]

> -----Original Message-----
> From: r-help-bounces@...
> [mailto:r-help-bounces@...] On Behalf Of azzza
> Sent: Tuesday, October 16, 2007 12:49 PM
> To: r-help@...
> Subject: Re: [R] Need some help
>
>
>
> THANKYOU guyz! yes, Jim's code was right (it was similar to someone
> elses)....I somehow missed his reply!
> Yes, that was exactly what i was looking for. lastly, how do
> i find the
> frequency of heads perhaps?
>

Could you post the code you finally settled on?

Dan

Daniel J. Nordlund
Research and Data Analysis
Washington State Department of Social and Health Services
Olympia, WA  98504-5204
 
 

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[tlumley]

On Tue, 16 Oct 2007, azzza wrote:

>
> Thats what is frustrating me....I've done a lot of reading, but there doesnt
> seem to be much info on sign changes..............I  dont udnerstand why the
> poportion of sign changes is much less than 50%, despite the proportion of
> heads being equal to that of tails.
>


I think some earlier posters have misunderstood what you are trying to do: they thought you were interested in runs of heads of tails, but it seems to me that you are interested in whether the sample proportion is above or below 1/2.

Code to compute the number of sign changes looks like

x<-rbinom(1000,1,0.5)
proportion <- cumsum(x)/(1:1000)
above <- proportion > 1/2
nchanges<-length(rle(above)$values)

You might also want to plot the cumulative sum

plot(1:1000, cumsum(x))
abline(h=0)

Looking at the plot you should be able to see why the number of changes is relatively small: to get a sign change you need the curve to go in the right direction (50:50) but you also need to be close enough to zero.


         -thomas

> Marc Schwartz wrote:
>>
>> You might want to do some more research on "Bernoulli Trials" and "Fair
>> Coins", which would provide some enlightenment on why you would not
>> "expect" 500 sign changes in 1,000 tosses and why you should, if the
>> coin is "fair", expect to *approach* a 50/50 distribution of heads and
>> tails in a large number of tosses, but not actually observe it.
>>
>> HTH,
>>
>> Marc Schwartz
>>
>>
>> On Tue, 2007-10-16 at 09:05 -0700, azzza wrote:
>>>
>>> You are right, I was a bit too vague. I am trying to simulate 1000 coin
>>> Tosses. Then to write a code for the number of heads/Tails.....naturally,
>>> we
>>> would expect the proportion of heads to be 50% so the number of heads
>>> would
>>> be around 500. Secondly, I'm trying to look at the number of sign changes
>>> in
>>> 1000 tosses. The example in the book shows that the number of sign
>>> changes
>>> is WAY less than 50%. so I was  trying to look for a code that shows the
>>> number of sign changes, which someone pointed out would be to use
>>> rle(x).....my concern however is that when the rle(x) is used, the
>>> proportion of sign changes is about 50% (around 500), which would be
>>> logical
>>> to expect, however, real life experiments have shown that the number of
>>> sign
>>> changes is actually much less than 50%. The other thing I was trying to
>>> do
>>> is to plot a line graph of number of sign changes versus the number of
>>> tosses. Yes, the number of tosses should begin at zero, and at zero coin
>>> toss, the sign change is zero. The range of the number of sign changes in
>>> the Y-axis should include negative values of Y. So, for toss number zero,
>>> the sign change is 0, for the first toss, the sign change may be +3 for
>>> instance, for the 50th toss, the sign change may be -5 for instance. The
>>> plot shown in the book shows that for most of the tosses, the sign
>>> changes
>>> were negative, and this would explain how the overall number of sign
>>> changes
>>> is very low.
>>>
>>> so basically, i was looking for a code to show the number of sign
>>> changes,
>>> and a plot of sign changes versus toss number (from toss #0 to toss
>>> number
>>> 1000). The Y axis (number of sign changes, should include negative values
>>> of
>>> Y)
>>>
>>> thanks
>>>
>>>
>>>
>>> Daniel Nordlund wrote:
>>>>
>>>>> -----Original Message-----
>>>>> From: r-help-bounces@...
>>> [mailto:r-help-bounces@...]
>>>>> On Behalf
>>>>> Of azzza
>>>>> Sent: Monday, October 15, 2007 6:06 PM
>>>>> To: r-help@...
>>>>> Subject: Re: [R] Need some help
>>>>>
>>>>>
>>>>>
>>>>> Thanks Jholtman.
>>>>> However, the plot didnt come out the way I envisone dit to be. On the
>>> Y
>>>>> axis, i should have sign changes in 1000 tosses, the range being from
>>>>> negative to postitive, and a straight horizontal line across  y=0. The
>>>>> X-axis should have the toss number, range 0-1000
>>>>>
>>>>
>>>> You would probably get more prompt and useful help if you would provide
>>> a
>>>> small, self- contained example of what you wanted (maybe small enough
>>> that
>>>> you could work it by hand).  Also, if you provided some code using the
>>>> help that you have already received, that would show that you are
>>> trying
>>>> to solve the problem yourself and others could help with the specific R
>>>> program issues that you are having.  For example, it is not clear to me
>>> if
>>>> you want to count the first run of tosses as 0 or 1 sign change.  I
>>> will
>>>> assume it is zero.  So with that assumption, does this get you what you
>>>> want?
>>>>
>>>> n <- 1000
>>>> x <- sample(c(0,1), n, TRUE)
>>>> y <- rle(x)
>>>>
>>>> z <- rep(1:length(y$lengths),y$lengths)
>>>> plot(1:n,z-1)
>>>>
>>>> Hope this is helpful,
>>>>
>>>> Dan
>>>>
>>>> Daniel Nordlund
>>>> Bothell, WA USA
>>>>
>>>> ______________________________________________
>>>> R-help@... mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>>
>>>
>>
>> ______________________________________________
>> R-help@... mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>
> --
> View this message in context: http://www.nabble.com/Need-some-help-tf4624513.html#a13238567
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Thomas Lumley Assoc. Professor, Biostatistics
tlumley@... University of Washington, Seattle

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[J Dougherty]

Azza,

By "sign changes" are you looking at how long runs of similar results are
before switching, e.g. HHTHTTTH sees four changes, while HHHHTTTT sees just
one?  

JD

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