Translation 5099

ISSN 0704-3716
Canadian Translation of Fisheries and Aquatic Sciences
No. 5099
A BASIC program to analyze the polymodal frequency
distribution into normal distributions
T. Akamine
Original title:
Polymodal-na Dosu Bunpu o Seiki Bunpu e Bunkai suru Basic Purgguramu
In: Bull. Jpn. Sea Reg. Fish. Res. Lab. (33): 163-166, 1982
Original language: Japanese'
Available from:
Canada Institute for Scientific and Technical Information
National Research Council
Ottawa, Ontario, Canada R1A 0S2
1984
6 typescript pages
,
V
II lee
Secretary
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' of
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Translated from - Traduction de
TrA5 5.0q
Into - En
English
Japanese
Author - Auteur
Tatsuro AKAMINE
Title in English or French - Titre anglais ou français
A BASIC Program to Analyze the Polymodal Frequency Distribution into Normal Distributions
Title in foreign language (Transliterate foreign characters)
Titre en langue étrangère (Transcrire en caractères romains)
Polymodal-na Dosu Bunpu o Seiki Bunpu e Bunkai suru Basic Puroguramu
Reference in foreign language (Name of book or publication) in full, transliterate foreign characters.
Référence en langue étrangère (Nom du livre ou publication), au complet, transcrire en caractères romains.
Nihonkai-ku Suisan Kenkyusho Hokoku
Reference in English or French - Référence en anglais ou français
Bulletin of the Japan Sea Regional Fisheries Research Laboratory
Publisher - Editeur
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1982
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Japanese
A BASIC Program to Analyze the Polymodal Frequency
Distribution into Normal Distributions
Tatsuro AKAMINE
1)
Abstract
The algorithm of this program is an iteration method which consists of the linear approximation and the method of least—squares.
Variables are modified one after another.
This program can be run on a micro computer,
although it takes a longer time in comparison
with larger computers.
UNEDITED TRANSLAMIA
TRADIJUiON le:1N RsvTir:E
infzrrnai. irin zetikcnt
Analyzing the polymodal frequency distribution into normal distribution is a fundamental method used when for instance dealing with
animal species the age character of which is not known. Although several
large computer programs have already been presented, researchers unable
to use the above depend on such methods as that of Tanaka (1956).
This basic program has been conceived for the presently marketed
small computers of less than e100.000, and a 2K bite memory is sufficient.
The calculating method which follows Shimadzu (1980) is that of linear
approximation and of the least squares. The parameters are moved one at a
time so as to minimize the memory.
The fact that it takes time is a
disadvantage but one has no choice but to take into consideration the
performance of the small computers in question.
1) Japan SeaRegional Fisheries Research Laboratory, Suido-cho, Niigata 951, Japan.
SEC 5-25 (Rev. 82/11)
CanadI3
- 2 Method of calculating
Let us call F the given frequency distribution, m the number of
classes, h the width of the classes, a the smallest class value and b the
greatest value.
denoted by n.
The number of normal distributions to be analyzed is
The sought formulai, the residual functions d
2 are then:
f =jKi. N (pi,
1
/27ra
N
x=.
ee l
j
(x— p) 2
1
2a2
.dx2=E (F—f) 2 —Cg)
Fi5,
b = a + (m —1) h
a
h
X
1
El smuyey]
Fig. 1. Illustration of variables.
The linear approximation o
2-1-'7
j
r
af
gives:
j .1_2/Jai
1aR- i 4K' +a-af
--, i l's 2ai 1
•
:if(i :.=_N (pi, ci, x)
af =Ki • N (pi, ai, x) • e— ili
2 1
p' .
cc i
Cl
• IV (pi, ui,x)
(X —
pi) 2 —ai 2
cri3
2
In order to minimize d , we make the parameters change in the
order.
If we indicate by a the parameter made to change we have:
ace
-
Jo-
- 3 -
By substituting in
d,
— (f+4.1.)} '-= (d.—
_iit4a)2
When using here the least square method, we obtain:
ee —o
ala
o
.(cr.M1
This is the corrected amount we are seeking.
Example of application
Using a MB 6880 microcomputer, we analyzed the body length
composition of porgy by Tanaka (1956).
d 2 is shown in Graph 2.
The state of convergence of
The results are shown in Table 1.
in Fig. 3 is obtained by plotting X-Y.
average of about 8 min for one time.
The Graph
With the MB 6880, it took an
When finishing in 10 times, it
takes about 80 min.
Discussion
With the present program, one must first put in the number
of normal distributions and the initial values. As good initial values
are put in data with clear modes, less time is needed. When to the
contrary putting in bad initial values and data with no clear modes,
vibrations and dispersion will frequently occur and there is a
possibility of entering a stop point. This program is used to achieve
objectivity and one must give plenty of consideration to input and
output.
4
Improvement points of this program
1) improving the input, output
2) improving the loop escape judgement.
At the close of this article, I wish to thank Fumihiko KATO,
researcher responsible at the Resource Department of the Japanese Sea
Regional Fisheries Laboratory, for drawing the chart based on the
plotting of X-Y and for giving us much advice.
e,
1.
Number of Iterations
Mqr* d'offliute
Fig. 2. Convergence of d.
nag
FORK LENGTH
0113M
..e401,#R4E.Te.
e") rDitt.:EK5145 t toeiontle
IN CM
1'1
OD
BASIC 7' e
-
Fig. S. Fork length frequency curve of porgy. The histogram shows the
observed frequenXcy, lines normal curves and the sum of each
normal curves fitted by this BASIC program.
.41
--e
5
••■•
2 ,ithiz umnoreR
ON 1
Table 1. Comparison of the results
from two methods.
2
1
3
4
5
cP
K5000400030001000500
initial
27
15.5 20
24
value ir 11
1.5 1.5 1.5 758923
1
)12' 1
K 5676 4331 2703 798 492
value after
29
p 11.0215.2719.8223.4626.66
iterations a 0.8231.1621.4781.2021.4756314
TANAKA'S
graphical
method
K 5627 4485 2630 840 461
10.9915.2619.8423.5026.82
0.8 1.2 1.4 1.2 1.4 19192
Correspondence of variables
14 :numberofnormaldistributions
A : Minimum class mark
H :class width
M number of classes
I)(1,J) K1
81
D(2,1) :II;
I:11:d.
I)(3,J)
112 :d.
:fri
•
F (X)
9.0
J- 9
Program list
F.,
G1: 0L
A2 : da
e 05' — P 7‘11f4U)
(DATA : an exampkof porgy)
REM POLVMODAL
REM :0019
READ N.A.M,H
PRINT N= • 10
PRINT '4= . 1A50
60 PRINT '11='10
70 PRINT • H • 114
80 DIM 013,01,F(M)
90 STOP
100 FOR 1=1 TO M
110 READ FM:PRINT 'F( . :11')= . tFt1/ •
120 NEXT I
10
20
30
40
130 SIOP
140 FOR J=1 TO N
150 FOR 1=1 TO 3
160 READ DCI.J/tPRINT
170 NEXT 1s56XT J
180 STOP
190 READ 091PRINT '09= . 109
200 STOP
210 REM 141)
220 D7=1
230 FOR 1=1 TO 3
240 FOR J=1 TO N
250 02=0: 5 1=0182=0
260 FOR 5 =1 10 14
270 0=14e(K-1I=H
280 F1=0
290 FOR L=1 TO N
300 P1=011.1):P2=X-0(2,L)1P3=0(3,1)
• 310 91=91e1 1 ■ .39C^42:73«E.St-.5=FZ , P2,P3/F3)
320 NEXT L
130 01=F(10-F1
340 01=13(1,J)s02=X-0(2,J)t03=0(3,J)
350 01=.398942/03.ExPI-.51.02+02/03/031
360 ON 1 GOTO 390.370,380
370 GI=C11..G1=02/03/031G0T0 390
380 01=01«01..(02•02-03=03)/03/03/03
390 02=02.01=01
400 S1=014E0001
410 S2=52.61=01
420 NEXT K
430 14 2= 5 1/S2
440 0i1.J>=0(1,J).02
450 PRINT
460 PRINT 137='107
470 PRINT • 1='11, • ,.1=';J
480 PRINT '02='032.'A2='1A2
490 NEXT JsNEXT I
500 07=07+1
510 IF 07<=09 GOTO 230
520 REM 51 5 9,9
530 PRINT
540 FOR J=1 TO N
550 FOR 1=1 10 3
560 PRINT 13I . ;11 . ..001=';011,J1
570 NEXT IINEXT J
500 ENÛ
1000 DATA 5.7.5,29.1
1010 DATA 7.79.509.2240.2341.623,476.1230.1439
1020 DATA 921.448,512,719.673.445.341.310.228
1030 DATA 168,140.114.64,22,0,2.2.0.0.1
1040 DATA 5000.11.1.4000,15.5.1,3000,20.1.5
1050 0010 1000,24.1.5,500.27.1.5
1060 DATA 30
6
Bibliography
Yasuhiko SHIMAZU
Taicho Sosei kara Nenrei Sosei o Suitei suru Hoho
(Method of evaluating the age composition from the body length composition)
Showa 54 nendo Gyogyo Shigen Kenkyu Kaigi, Nishi Nihon Teigyo Bukai Kaigi
Hokoku
(The 1979 report from the Western Japan Bottom Fish Branch Conference,
Fisheries Resources Research Council):
Shoichi TANAKA (1956)
36-48.
Polymodal-na Dosu Bunpu no Hitotsu no Toriatsukaikata
oyobi sono Kidai Taicho Sosei Bunseki e no Oyo (One way of handling
polymodal frequency distribution and application to the analysis of porgy
body length composition)
Tokaisuiken Hokoku (abbreviated title;
from the Eastern Fisheries Laboratory)
(14): 1-13.
e
eatVi1:(1979). f*R411. ■1a , r7ink1591
venef-ensequng-ir.
miEl*ItAteeezegei: 36-48.
Polymodal leltekiT
- eop — °
(03i3ZIECRZY-Ice)
eRtibegtn-N
ape-A. *ei(lifulifef (14) :1-13.
report