| 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 | 
               ....
             ..    ..
           ..        ..
         ..            ..
        .                ..
       .                   ..
      .                      ..
     .                         ..
     .                           ...
    .                               ...
    .                                  ...
    ----------------------------------------
    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 11:44 | 16 | 
| Seems like the radiation spectrum of a black body.
I'll look up the generating equation and let you know tomorrow...
Intensity
    ^          ....
    |        ..    ..
    |      ..        ..
    |    ..            ..
    |   .                ..
    |  .                   ..
    | .                      ..
    |.                         ..
    |.                           ...
    .                               ...
    .                                  ...
    +------------------------------------------------> frequency
 | |||||
| 1677.2 | or look at gamma densities | SGOUTL::BELDIN_R | D-Day: 161 days and counting | Wed Oct 21 1992 12:34 | 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
 | |||||
| 1677.3 | HERON::BUCHANAN | The was not found. | Wed Oct 21 1992 13:07 | 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 13:23 | 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� 
    
 | |||||
| 1677.5 | 3D::ROTH | Geometry is the real life! | Wed Oct 21 1992 13:41 | 4 | |
|     It may be a Rayleigh distribution, essentially a chi squared
    distribution of 2 degrees of freedom.
    - Jim
 | |||||
| 1677.6 | RUSURE::EDP | Always mount a scratch monkey. | Wed Oct 21 1992 14:22 | 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
 | |||||
| 1677.7 | >2 df. | CADSYS::COOPER | Topher Cooper | Wed Oct 21 1992 14:58 | 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
 | |||||
| 1677.8 | STAR::ABBASI | I love DECspell | Wed Oct 21 1992 15:38 | 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
 | |||||
| 1677.9 | a little bit closer :-) | CSC32::D_DERAMO | Dan D'Eramo, Customer Support Center | Wed Oct 21 1992 21:14 | 10 | 
|     re .-1,
    
>           -
>    like   A  , but the dash is close to the A ? 
    
			_
    How about this:	A
    
    Dan
    0:-)
 | |||||
| 1677.10 | not BB but x*exp(-x) | BRSTR2::SYSMAN | Dirk Van de moortel | Thu Oct 22 1992 04:42 | 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
 | |||||
| 1677.11 | AYOV11::IGILLESPIE | Thu Oct 22 1992 04:48 | 15 | ||
|     
    
    Looks like a Poisson distribution.
    
             -m  x
            e   m
    P(x)= ----------
              x!
    
    
    Where m = average number of occurancies
          e = e ... (2.71828...)
    
    
    Iain
 | |||||