Math problem - Gaussian curves

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Math problem - Gaussian curves

Author

Topic

SamC
White Water Yakist

3467 Posts

Posted - 2004-03-18 : 14:00:16

I've got data representing counts versus time. Starting at T=0, the counts rise very gradually. There's a no clear peak, and the curve drops to zero in a few hours. The data is asymmetric and doesn't look vaguely gaussian.

Gaussian curves are described by: Average and Standard Deviation, but are aggregate functions in SQL.

Is there a better representation of a curve that has a zero point, peak and a long tail?

Sam


Time    Count
0	188
5	980
10	1045
15	851
20	692
25	620
30	538
35	518
40	469
45	407
50	376
55	387
60	310
65	281
70	244
75	217
80	192
85	166
90	153
95	138
100	107
105	87
110	103
115	77
120	63
125	50
130	43
135	49
140	40
145	33
150	27
155	26
160	21
165	18
170	16
175	9
180	10
185	6
190	8
195	9
200	2
205	6
210	4
215	3
220	5
225	1
230	5
235	1
240	3
245	3
250	3
255	3
260	2
265	1
270	1
275	2
280	2
290	1
300	1
310	1
355	1

X002548
Not Just a Number

15586 Posts

Posted - 2004-03-18 : 14:34:14

OK, I gotta ask...what he h_ll are you working on?

Spaceflight?

Brett

8-)

EDIT: http://www.duke.edu/~loeb/spring.2000/lab5.html

Still looking....

SamC
White Water Yakist

3467 Posts

Posted - 2004-03-18 : 14:51:42

Brett,

The numbers represent an event in nature which I cannot disclose.

Did you listen to Groove Salad?

Arnold Fribble
Yak-finder General

1961 Posts

Posted - 2004-03-18 : 14:56:09

Looks like LogNormal to me.

SamC
White Water Yakist

3467 Posts

Posted - 2004-03-18 : 15:00:53

A man of few words, but to the point.

Off too Google..

Looks Lognormal to me (too).

So it turns out that Mean and Standard Deviation do apply (to Lognormal curves).

But the additional information to describe the shape is the Skewness and the Kurtosis.

Learning somethin new every day.

Thanks Arnold.

Sam

Frank Kalis
Constraint Violating Yak Guru

413 Posts

Posted - 2004-03-18 : 16:07:11

As your links refer to risk glossary, just out of professional curiosity may I ask what you are working on? Some kind of financial risk management package?

--Frank
http://www.insidesql.de

SamC
White Water Yakist

3467 Posts

Posted - 2004-03-18 : 16:17:15

Nothing financial about the numbers at all. I'm reserved about going into detail about what the numbers actually represent, but I will say the numbers represent "usage". I was looking for a way to characterize the curve verbally (mean, Std Dev, etc.) without using a graphic or visual aids.

Of course, a stored procedure will calculate the curve parameters.

I think I have found what I was after.

Sam

Frank Kalis
Constraint Violating Yak Guru

413 Posts

Posted - 2004-03-18 : 16:26:17

Actually I was not interested in the number you provided.
Just because the terms you've used are quite familiar to my daily work, although I really guess no one outside the ivory tower cares in his investment decisions for such abstract constructions.
But if you are working on a formula that will exactly predict where some stock index will end this year, I'll organize the money, you the formula and we meet on the Cayman's.

OK?

--Frank
http://www.insidesql.de

SamC
White Water Yakist

3467 Posts

Posted - 2004-03-18 : 16:38:37

I'm there good buddy. Margaritas and palm trees. All we need is an *exact* predictor. Should be easy.

Frank Kalis
Constraint Violating Yak Guru

413 Posts

Posted - 2004-03-18 : 16:45:58

Ok, I can liquidate some 1 billion Euro quite easily. That's enough for drinks and aspirine.

--Frank
http://www.insidesql.de

Frank Kalis
Constraint Violating Yak Guru

413 Posts

Posted - 2004-03-19 : 01:52:57

Just for completeness.
Here is some fine TSQL code for skewness and curtosis from SQL Server MVP Steve Kass.


select sum((qty-mean)*square(qty-mean)
       /(N*sigma*square(sigma))) as skew,
       sum(square(square(qty-mean))
       /(N*square(square(sigma))))-3 as ExcessKurtosis
from pubs..sales,
(
  select
    avg(qty) as mean,
    stdev(qty) as sigma,
    count(qty) as N
  from pubs..sales
) S

skew                                                  ExcessKurtosis                                        
----------------------------------------------------- ----------------------------------------------------- 
1.5653251929405994                                    2.4599827492380095

(1 row(s) affected)

The original code along with some other very interesting stuff you'll find here
http://www.users.drew.edu/skass/sql/SkewKurtosis.sql.txt

--Frank
http://www.insidesql.de

SamC
White Water Yakist

3467 Posts

Posted - 2004-03-19 : 08:22:10

"Skewness" and "Curtosis" are names that are suggestive of personal characterizations. One day, they'll show up on a singles website.

Curtosis is an obvious factor that describes height to girth. You could filter out single candidates using weight and curtosis.

But "Skewness" while it could describe a physical imbalance would be a more appropriate characterization of a psychological element ......

For example, a skewness of zero might be a boring, but the most interesting people have a moderate skewness with solid emotional center. Large variances in skewness could be wierd or scary.

All that's needed is an *exact* equation.

Frank Kalis
Constraint Violating Yak Guru

413 Posts

Posted - 2004-03-19 : 08:27:36

--Frank
http://www.insidesql.de

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