A COMPUTER PROGRAM FOR ANALYSIS OF 



POLYMODAL FREQUENCY DISTRIBUTIONS 



(ENORMSEP), FORTRAN IV 



Program ENORMSEP (Extended Normal 

 Separator Program) separates a polymodal 

 frequency distribution into its component groups 

 where aging studies have not been or cannot be 

 performed. The program calculates preliminary 

 estimates of the number of size groups and their 

 points of overlap using probit analysis and 

 polynomial regression techniques. These 

 preliminary estimates are then entered into 

 NORMSEP (Normal Separator Program) (Has- 

 selblad 1966), used as a subroutine, in order to 

 complete the analysis. 



Output data are generated both as listings and 

 punched cards. Listings include at the option of 

 the user: 1) table of values of the standardized 

 normal distribution; 2) table of values of 

 probabilities, standardized normal variables, and 

 probits; 3) polynomial regressions and analyses of 

 variance of probits; 4) table of residuals for the 

 final regression; 5) table of roots corresponding to 

 all regressions after taking second derivative; 6) 

 tables for analyses for the separation of modes; 7) 

 plots of observed and predicted values for the final 

 regression; and 8) plot of the original frequency 

 distribution. Punched card output includes the 

 number of observed frequency distributions with 

 their intervals and probits and regression 

 coeflftcients for the polynomials. 



Input data require the observed size frequency 

 together with values for identification and control 

 purposes. No more than nine size groups may be 

 separated because of limits on the eflftciency of 

 parameter estimate in the polynomial regression. 



This computer program was developed on an 

 IBM 360/651 computer' using release 20.7 

 MVT/HASP system at the Statistical and Com- 

 puting Center at the University of Hawaii. This 

 computer program is capable of processing mul- 

 tiple sets of data. For a "typical" problem, the 

 program takes about 1 min of central processing 

 unit time and a total machine unit time of 1.5 min 

 to run a single problem "individually." The 

 requirement for core storage is 168K, where K is 

 1,024 bytes and where a byte is an address collec- 



tion consisting of eight binary bits or binary 

 digits. 



A description of the program, including 

 program listing as well as input and output for two 

 examples, is available from the authors upon 

 request. 



Literature Cited 



Hasselblad, v. 



1966. Estimation of parameters for a mixture of normal 

 distributions. Technometrics 8:431-444. 



Marian Y. Y. Yong 

 Robert A. Skillman 



Southwest Fisheries Center Honolulu Laboratory 

 National Marine Fisheries Service, NOAA 

 Honolulu, HI 96812 



'Reference to this particular computer system does not imply 

 endorsement of the product by the National Marine Fisheries 

 Service, NOAA, but is given to provide the reader with a base for 

 determining the cost of performing jobs with the particular 

 computer system at his disposal. 



RECORDS OF LARVAL, TRANSFORMING, 



AND ADULT SPECIMENS OF THE QUILLFISH, 



PTILICHTHYS GOOD EI, 



FROM WATERS OFF OREGON 



This report extends the southern range of the 

 quillfish, Ptilichthys goodei Bean 1881, in the 

 northeast Pacific to waters off the central coast of 

 Oregon where larval, transforming, and adult 

 specimens have been collected. The previously 

 reported range of this species in the North Pacific 

 was from the Okhotsk and Bering seas to northern 

 Washington and Puget Sound (DeLacy et al. 1972; 

 Quast and Hall 1972; Hart 1973). The life history of 

 the quillfish is poorly understood and nothing is 

 known of the early stages (Walker 1953; Makushok 

 1958; Grinols 1965; Hart 1973). 



Materials and Methods 



Three larvae (20.3, 24.7, 36.0 mm SL-standard 

 length) and one transforming specimen (114 mm 

 SL) of P. goodei came from plankton collections 

 made with large-mouth (0.7 m) bongos having 

 0.571-mm mesh nets. Tows were made in a step- 

 oblique or oblique manner from near the bottom or 

 150 m (at deeper stations) to the surface at a vessel 

 speed of 2 knots. Tow times were 16 to 25 min. The 

 specimens were fixed in 10% and stored in 5% buf- 

 fered Formalin.' 



'Reference to trade names does not imply endorsement by the 

 National Marine Fisheries Service, NOAA. 



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