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braylcdf

PURPOSE ^

Beta Rayleigh CDF of wave heights

SYNOPSIS ^

y = braylcdf(x,a,b,c)

DESCRIPTION ^

 BRAYLCDF Beta Rayleigh CDF of wave heights 
        /h               
    F = | 2*(a+b-1)!/((a-1)! * (b-1)!)*x^(2a-1)*(1-(x/c)^2)^(b-1)/c^(2a) dx 
        /0                 
  
   CALL:  F = braylcdf(h,a,b,c)  
  
        F = cdf 
        h = waveheigth (0 <= h <= c) 
        a = abs(k1*(k2-k1)/(k1^2-k2))  
        b = abs(1-k1)*(k2-k1)/(k1^2-k2))  
        c = Hb, breaking wave height approximated by water depth, d. 
  where 
       k1 = E(H^2)/Hb^2 
       k2 = E(H^4)/Hb^4 
   E(H^2) = .5*exp(0.00272*(d/g*Tp^2)^(-0.834))*Hm0^2 
   E(H^4) = .5*exp(0.00046*(d/g*Tp^2)^(-1.208))*Hm0^2 
      Hm0 = significant waveheight 
      Tp  = modal period of wave spectrum 
  
     The size of F is the common size of H, A, B and C.  A scalar input    
     functions as a constant matrix of the same size as the other input. 
  
  Example: % Compare with rayleigh distribution 
   Hm0 = 7;Tp = 11;d = 50; g = gravity; 
   k1  = .5*exp(0.00272*(d/g*Tp^2)^(-0.834))*Hm0^2/d^2; 
   k2  = .5*exp(0.00046*(d/g*Tp^2)^(-1.208))*Hm0^2/d^4; 
   a   = abs(k1*(k2-k1)/(k1^2-k2));  
   b   = abs((1-k1)*(k2-k1)/(k1^2-k2)); 
   h   = linspace(0,2*Hm0)'; 
  semilogy(h,1-braylcdf(h,a,b,d),'r',h,1-wraylcdf(h,Hm0/2)) 
  
  See also  wbetacdf

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function y = braylcdf(x,a,b,c) 
002 %BRAYLCDF Beta Rayleigh CDF of wave heights 
003 %       /h               
004 %   F = | 2*(a+b-1)!/((a-1)! * (b-1)!)*x^(2a-1)*(1-(x/c)^2)^(b-1)/c^(2a) dx 
005 %       /0                 
006 % 
007 %  CALL:  F = braylcdf(h,a,b,c)  
008 % 
009 %       F = cdf 
010 %       h = waveheigth (0 <= h <= c) 
011 %       a = abs(k1*(k2-k1)/(k1^2-k2))  
012 %       b = abs(1-k1)*(k2-k1)/(k1^2-k2))  
013 %       c = Hb, breaking wave height approximated by water depth, d. 
014 % where 
015 %      k1 = E(H^2)/Hb^2 
016 %      k2 = E(H^4)/Hb^4 
017 %  E(H^2) = .5*exp(0.00272*(d/g*Tp^2)^(-0.834))*Hm0^2 
018 %  E(H^4) = .5*exp(0.00046*(d/g*Tp^2)^(-1.208))*Hm0^2 
019 %     Hm0 = significant waveheight 
020 %     Tp  = modal period of wave spectrum 
021 % 
022 %    The size of F is the common size of H, A, B and C.  A scalar input    
023 %    functions as a constant matrix of the same size as the other input. 
024 % 
025 % Example: % Compare with rayleigh distribution 
026 %  Hm0 = 7;Tp = 11;d = 50; g = gravity; 
027 %  k1  = .5*exp(0.00272*(d/g*Tp^2)^(-0.834))*Hm0^2/d^2; 
028 %  k2  = .5*exp(0.00046*(d/g*Tp^2)^(-1.208))*Hm0^2/d^4; 
029 %  a   = abs(k1*(k2-k1)/(k1^2-k2));  
030 %  b   = abs((1-k1)*(k2-k1)/(k1^2-k2)); 
031 %  h   = linspace(0,2*Hm0)'; 
032 % semilogy(h,1-braylcdf(h,a,b,d),'r',h,1-wraylcdf(h,Hm0/2)) 
033 % 
034 % See also  wbetacdf 
035  
036 %  
037 %   Reference: 
038 %       Michel K. Ochi (1998), 
039 %      "OCEAN WAVES, The stochastic approach", 
040 %       OCEAN TECHNOLOGY series 6, Cambridge, pp 279. (pd of peaks to trough)  
041  
042 % tested on: matlab 5.x 
043 % History: 
044 % Revised pab 31.03.2001  
045 %  added example 
046 % revised pab 14.10.1999 
047 % updated help header 
048 %  Per A. Brodtkorb 21.02.99 
049 error(nargchk(4,4,nargin)) 
050  
051  
052 [errorcode, x, a, b, c] = comnsize(x,a,b,c); 
053 if errorcode > 0 
054     error('h, a, b and c must be of common size or scalar.'); 
055 end 
056  
057  
058 % Initialize Y to zero. 
059 y=zeros(size(x)); 
060  
061 % Return NaN if A,B or C  is not positive. 
062 k1 = find(a <= 0| b<=0|c<=0); 
063 if any(k1)  
064     tmp   = NaN; 
065     y(k1) = tmp(ones(size(k1))); 
066 end 
067  
068 k=find(a > 0 & x >0 & b>0 & c>0); 
069 if any(k), 
070   xk = x(k); ak = a(k); bk = b(k);ck=c(k); 
071   y(k)=wbetacdf((xk./ck).^2,ak,bk); 
072 end 
073  
074  
075  
076  
077

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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