MATLAB: Definite Sum of density functions

sum symsum density

I need to compute :

Sum (from n=1 to N) [dgamma(x,n)*(1-dgamma(k,n))]

Sorry for the form I don't managed to do something esthetic.

Have you got an idea ? I have tried this in vain :

% Try 1
N = 100;
S = 0;
for n = 1:N
  S = S + (dgamma(x,n)*(1-dgamma(k,n)));
end
% Try 2
N = 100;
syms n m
S = symsum(dgamma(x,n)*(1-dgamma(k,n)),n,1,N);

Best Answer

See the documentation on the Gamma Distribution.

Related Solutions

MATLAB: How to plot this implicit function

Try symbolic expression

clc,clear
alpha=1.5; A=0.0207; gamma=0.25;
syms beta eps
x = (beta-alpha*(beta-gamma)+sqrt((beta-alpha*(beta-gamma)).^2+4*alpha*beta*gamma*A))./(2*beta);
y =  x.*(1-x).*beta/gamma;
t =  -x+x.*y.*(alpha-eps*beta)./((A+x+y).^2);
d =  eps*beta.*x.*y.*(x.^2+(A+x).*x+A*alpha)./((A+x+y).^3);
    % convert symbolic expression to function handle
F = matlabFunction(t.^2 - d,'vars',[beta eps]);
ezplot(F,[0,1,0,1]);

MATLAB: Why does it take forever to solve a function

symsum is often the wrong function to call when you want to calculate a definite sum (that is, the upper and lower bound are numeric.) symsum() works by trying to calculate the general formula for the indefinite summation, and then substituting in the upper and lower bounds. Calculating the general formula can take a long time.

Instead, when you have numeric upper and lower bounds, you should typically generate all of the individual entries; vectorize if possible and otherwise use a for loop or arrayfun(). Then with those in hand, sum() the result.

I corrected some errors in your calculations of pd1

M = 8;
N = 32;
K = 14;
c = 2;
s = 1;
T = 18.623390280430364437245197384232;
nlambda = 50;
lambdavals = linspace(0,30,nlambda);
pd = zeros(1, nlambda);
for L = 1 : nlambda
    lambda = lambdavals(L);
    T1lambda = T./(1+lambda);                 %constant sub-expression factored out
    pd1temp = arrayfun(@(i) nchoosek(N/2,i) * gamma(K+i) * gamma(N-K-i+1+T1lambda), K : N/2, 'Uniform', 0); %constant denominator removed from terms
    pd1sum = sum( [pd1temp{:}] ) ./ gamma(N+1+T1lambda);      %this is the first symsum
    pd1 = 2 * K * nchoosek(N/2,K) * gamma(K) * gamma(N/2-K+1+T1lambda) / gamma(N/2+1+T1lambda) - pd1sum;
    pdtemp = arrayfun(@(i) nchoosek(M,i)*(pd1)^(i)*(1-pd1)^(M-i), s:M, 'Uniform' ,0);
    pdsum = sum( [pdtemp{:}] );                       %this is the second symsum
    pd(L) = pdsum;
  end
plot(lambdavals, pd)

You will find that this will take less than a second to compute.

Best Answer

Related Solutions

MATLAB: How to plot this implicit function

MATLAB: Why does it take forever to solve a function

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