| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
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Does this curve look familiar to anybody? Sort of a normal curve, but
squashed left? I'm looking for a statistical distribution and "know"
I've seen this before, but none of my college texts show this curve.
(Of course, they -all- show the normal curve, then list all the others).
If you can identify the curve, can you supply the generating equation?
John
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1677.1 | seems like a black body | BRSTR2::SYSMAN | Dirk Van de moortel | Wed Oct 21 1992 12:44 | 16 |
Seems like the radiation spectrum of a black body.
I'll look up the generating equation and let you know tomorrow...
Intensity
^ ....
| .. ..
| .. ..
| .. ..
| . ..
| . ..
| . ..
|. ..
|. ...
. ...
. ...
+------------------------------------------------> frequency
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| 1677.2 | or look at gamma densities | SGOUTL::BELDIN_R | D-Day: 161 days and counting | Wed Oct 21 1992 13:34 | 18 |
If you look at log-normal histograms, they will look like that,
positive, unimodal, and tailing off to infinity.
If X is log normal, then log X is normal. Let Y = log X. Assume Y is
Normal(�,�).
2 2
f(y)dy = k exp(-(y-�) /2� )dy.
2 2
f(log x)dlog x = k' exp(-(log x-�) /2� )(1/x)dx
where k and k' are defined so the integrals = 1.
Is that what you're after? You can find all kinds of curves that give
that shape, of course, but this is a common one in statistics.
Dick
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| 1677.3 | HERON::BUCHANAN | The was not found. | Wed Oct 21 1992 14:07 | 6 | |
Hey neat: � How d'you get that character? I don't spose there are any other Greek characters that we can get? (apart from �) Andrew. | |||||
| 1677.4 | kilroy was here and murphy too! | SGOUTL::BELDIN_R | D-Day: 161 days and counting | Wed Oct 21 1992 14:23 | 8 |
� is compose / u. and � is compose o /. and � is compose <<
There are more, but I can only find them by hacking and never when I
want them. I don't where you can get documentation. I have seen alpha
and sigma too, but I've broken my fingers trying to guess how.
�j�
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| 1677.5 | 3D::ROTH | Geometry is the real life! | Wed Oct 21 1992 14:41 | 4 | |
It may be a Rayleigh distribution, essentially a chi squared
distribution of 2 degrees of freedom.
- Jim
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| 1677.6 | RUSURE::EDP | Always mount a scratch monkey. | Wed Oct 21 1992 15:22 | 94 | |
Here's a list of the compose sequences.
-- edp
� A"
� a"
� A'
� a'
� A^
� a^
� A'
� a'
� AE
� ae
� A~
� a~
� A*
� a*
� a_
@ aa
� C,
� c,
� c/
� c0
� E"
� e"
� E'
� e'
� E^
� e^
� E`
� e`
� I"
� i"
� I'
� i'
� I^
� i^
� I`
� i`
� L-
� N~
� n~
� O"
� o"
� O'
� o'
� O^
� o^
� O`
� o`
� OE
� oe
� O~
� o~
� O/
� o/
� OX
� o_
� P!
� SO
� ss
� U"
� u"
� U'
� u'
� U^
� u^
� U`
� u`
� Y"
� y"
� Y-
� ^0
� ^1
� ^2
� ^3
� 12
� 14
[ ((
{ (-
] ))
} )-
� <<
� >>
� ??
� !!
� ^.
| ^/
# ++
� +-
\ //
� /u
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| 1677.7 | >2 df. | CADSYS::COOPER | Topher Cooper | Wed Oct 21 1992 15:58 | 18 |
RE: .5 (Jim)
Chi� looks like that -- but only for 3 or more degrees of freedom.
chi�[n](x) = x^((n-2)/2)*exp(-x/2)/(2^(n/2)*GAMMA(n/2));
The gamma distribution, for some choices of the parameters, will also
work:
gamma[a, b](x) = x^a*exp(-x/b)/(GAMMA(a+1)*b^(a+1))
which is hardly surprising since gamma[(n-2)/2, 2] = chi�[n]. So
basically you get an extra parameter to play with in fitting, and there
isn't even a hint that 'a' must be an integer.
My best guess is that you are remembering the log-normal, though.
Topher
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| 1677.8 | STAR::ABBASI | I love DECspell | Wed Oct 21 1992 16:38 | 8 | |
ref .6
Thanks EDP for that list, do you know if one can write vectors too?
-
like A , but the dash is close to the A ?
/nasser
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| 1677.9 | a little bit closer :-) | CSC32::D_DERAMO | Dan D'Eramo, Customer Support Center | Wed Oct 21 1992 22:14 | 10 |
re .-1,
> -
> like A , but the dash is close to the A ?
_
How about this: A
Dan
0:-)
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| 1677.10 | not BB but x*exp(-x) | BRSTR2::SYSMAN | Dirk Van de moortel | Thu Oct 22 1992 05:42 | 80 |
re. 1
3
x
It's not a black body spectrum: BB(x) = --------
x
e -1
which must have an horizontal tangent in (0,0), while yours clearly
has a vertical tangent...
-x
The simplest function I can think of with these properties is: x e
Here's a plot (made with good old datatrieve!) of that function:
If you have a graphics terminal (VT240,VT330,...) say EXTRACT TT:
<[2JP1p
s[0,0](EA[0,0][767,479]
S1I(D))p[0,0] @:B@;
T(A0S1)t(s1I0)w(vi(w)s0P1)
L(A2)
L"5"00FF8181818181FF
L"6"0018244281422418
L"0"00FF814242242418
T(B)
T(E)
P[100,360]V[+600][,-350][100][,360]
P[0,185]T(B)[0,25]""
T[15,0]P[133,460]T"x*exp(-x) -- Control_W to resume..."T(E)
P[81,355]T"0"
P[101,273]V(W(P4I(0)))[+598]
P[45,268]T" .100"
P[101,185]V(W(P4I(0)))[+598]
P[45,180]T" .200"
P[101,98]V(W(P4I(0)))[+598]
P[45,93]T" .300"
P[45,5]T" .400"
P[96,375]T"0"
P[200,359]V(W(P4I(0)))[,-348]
P[196,375]T"1"
P[300,359]V(W(P4I(0)))[,-348]
P[296,375]T"2"
P[400,359]V(W(P4I(0)))[,-348]
P[396,375]T"3"
P[500,359]V(W(P4I(0)))[,-348]
P[496,375]T"4"
P[600,359]V(W(P4I(0)))[,-348]
P[596,375]T"5"
P[696,375]T"6"
T(BA2S[8,16])
P[105,318]W(I1)
V[105,318]V[110,281]V[115,247]V[120,217]V[125,190]V[130,166]V[135,144]V[140,125]
V[145,109]V[150,95]V[155,82]V[160,72]V[165,63]V[170,56]V[175,50]V[180,45]
V[185,42]V[190,40]V[195,39]V[200,38]V[205,38]V[210,40]V[215,41]V[220,44]
V[225,47]V[230,50]V[235,54]V[240,58]V[245,62]V[250,67]V[255,72]V[260,77]
V[265,83]V[270,88]V[275,94]V[280,100]V[285,105]V[290,111]V[295,117]V[300,123]
V[305,129]V[310,135]V[315,141]V[320,147]V[325,152]V[330,158]V[335,164]V[340,169]
V[345,175]V[350,180]V[355,186]V[360,191]V[365,196]V[370,201]V[375,206]V[380,211]
V[385,216]V[390,220]V[395,225]V[400,229]V[405,234]V[410,238]V[415,242]V[420,246]
V[425,250]V[430,253]V[435,257]V[440,261]V[445,264]V[450,268]V[455,271]V[460,274]
V[465,277]V[470,280]V[475,283]V[480,286]V[485,288]V[490,291]V[495,293]V[500,296]
V[505,298]V[510,301]V[515,303]V[520,305]V[525,307]V[530,309]V[535,311]V[540,313]
V[545,315]V[550,316]V[555,318]V[560,320]V[565,321]V[570,323]V[575,324]V[580,325]
V[585,327]V[590,328]V[595,329]V[600,331]V[605,332]V[610,333]V[615,334]V[620,335]
V[625,336]V[630,337]V[635,338]V[640,339]V[645,340]V[650,340]V[655,341]V[660,342]
V[665,343]V[670,343]V[675,344]V[680,345]V[685,345]V[690,346]V[695,346]V[700,347]
W(R)
p[101,308]t"6"
p[696,337]t"6"
T(E)
@:B W(I0S1)P[,-30]V[+56]W(I3S0)
V[,+30][-56][,-30][+56]P(B)
P(E)[-52,+20]
P(B)[,+0]
[,-16]W(I1)T(A2S[8,20])
"6"P[+4]
W(I3)T(A0)[12,0]"Y1"P(E)
@;
P[102,40]@B
W(I(W))P[,500]\[1;24r[24;0f [20;0f
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| 1677.11 | AYOV11::IGILLESPIE | Thu Oct 22 1992 05:48 | 15 | ||
Looks like a Poisson distribution.
-m x
e m
P(x)= ----------
x!
Where m = average number of occurancies
e = e ... (2.71828...)
Iain
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