Re: Re: Unexpected Characters Appearing in
- To: mathgroup at smc.vnet.net
- Subject: [mg103308] Re: [mg103291] Re: [mg103263] Unexpected Characters Appearing in
- From: Gregory Lypny <gregory.lypny at videotron.ca>
- Date: Mon, 14 Sep 2009 07:12:18 -0400 (EDT)
- References: <20090913102455.L99QL.153756.imail@eastrmwml38>
Guess it's something to do with my machine or my version of
Mathematica (7.0.1). I may delete Mathematica's preference file.
Maybe it's corrupt.
Gregory
On 2009-09-13, at 10:24 AM, Bob Hanlon wrote:
>
> I don't see any exclamation marks in the output
>
> $Version
>
> 7.0 for Mac OS X x86 (64-bit) (February 19, 2009)
>
> stdDev[x_] :=
> Sqrt[Plus @@ (Plus[#, -Mean@x]^2 & /@ x)/Length@x]
>
> What you are calling the standard deviation is a biased estimator of
> the standard deviation of the total population (from which your
> sample is drawn). This estimate is the root mean square of the
> deviation from the mean.
>
> data = {a, b, c, d, e};
>
> stdDev[data] ==
> RootMeanSquare[data - Mean[data]] ==
>
> Sqrt[Total[(data - Mean[data])^2]/Length[data]]
>
> True
>
> The unbiased estimator of the standard deviation of the population
> is StandardDeviation
>
> StandardDeviation[data] ==
>
> Sqrt[Total[(data - Mean[data])^2]/(Length[data] - 1)] //
>
> Simplify[#, Element[data, Reals]] &
>
> True
>
> p = {{107, 138}, {119, 129},
> {104, 101}, {107, 91}, {123, 94}};
>
> StandardDeviation /@ Transpose[p] // N
>
> {8.42615,21.4546}
>
> stdDev /@ Transpose[p] // N
>
> {7.53658,19.1896}
>
> Note that the biased estimate under-estimates the standard deviation
>
> r = Differences@p/Most@p;
>
> StandardDeviation /@ Transpose[r] // N
>
> {0.122332,0.103158}
>
> stdDev /@ Transpose[r] // N
>
> {0.105942,0.0893377}
>
>
> Bob Hanlon
>
> ---- Gregory Lypny <gregory.lypny at videotron.ca> wrote:
>
> =============
> Hi Bobby,
>
> Yeh, you're right. Kind of skimped on the details. Sorry about that.
>
> Here's some data, five observations each on the prices of two stocks.
> First element in each is stock 1 and the second element is stock 2.
>
> p= {{107, 138}, {119, 129}, {104, 101}, {107, 91}, {123, 94}}
>
> Here's a function for computing standard deviation that goes down each
> "column" as it were. I think a version of this was suggested on
> MathGroup.
>
> stdDev[x_] := Sqrt[Plus @@ (Plus[#, -Mean@x]^2 & /@ x)/Length@x]
>
> The standard deviation of price is not a problem.
>
> {7.53658, 19.1896}
>
> Now I convert the prices to returns,
>
> (r = Differences@p/Most@p)
>
> {{12/107, -(3/46)}, {-(15/119), -(28/129)}, {3/104, -(10/101)},
> {16/107, 3/91}}
>
> leaving me with four observations each because of the differencing.
> Taking the standard deviation of returns gives me
>
> {0.105942 \.10, 0.0893377 \.10}
>
> where the \.10 appears when I copy from Mathematica and paste into my
> mail software, but in Mathematica, the \.10 appears as an exclamation
> mark (!) with what appears to be a skinny space between it and the
> last digit reported for each result.
>
> The answers for returns are correct, and the exclamation mark still
> appears if I compute r as a numerical approximation rather than
> rationals. Any thoughts?
>
> Regards,
>
> Gregory
>
>
>
> On 2009-09-12, at 1:47 AM, DrMajorBob wrote:
>
>> Details, Gregory. Details.
>>
>> Bobby
>>
>> On Fri, 11 Sep 2009 18:57:30 -0500, Gregory Lypny <gregory.lypny at videotron.ca
>>> wrote:
>>
>>> Hello everyone,
>>>
>>> I created a function to compute standard deviation, and in some
>>> instances it returns a result with an exclamation mark (!) at the
>>> end,
>>> as in
>>>
>>> 0.143855 !
>>>
>>> When the result is copied as plain text and pasted elsewhere, it
>>> comes
>>> out as
>>>
>>> 0.143855 \.10
>>>
>>> Any reason why this is happening? I recently upgraded my Mac to
>>> Snow
>>> Leopard, and thought that might be the cause.
>>>
>>> Regards,
>>>
>>> Gregory
>>>
>>
>>
>> --
>> DrMajorBob at yahoo.com
>