I would like to calculate and to plot the following equation:
f(t,x) = (beta_hat*s(t,x)*[I(t,x)]^(beta_hat-1))*exp(-[I(t,x)]^beta_hat)
s(t,x): step-function(330 for x=[0;2000])
(350 for x=[2000;3000])
(390 for x=[3000;4000])
I(t,x): Integral(exp(-B_hat/x(u))/C_hat)) from x=0 to t
beta_hat, C_hat and B_hat are known parameters
My MATLAB-script looks like that:
beta_hat = 4.2915822
B_hat = 1861.6186657
C_hat = 58.9848692
y(t) = (exp(-B_hat/((heaviside(t)-heaviside(t-2000))*(330)+(heaviside(t-2000)-heaviside(t-3000))*(350)+...
f = @(x)(beta_hat*fnum(x).*Inum(x).^(beta_hat-1)).*exp(-(Inum(x).^beta_hat))
But if I plot my function f the figure isn´t right. There should be a smooth curve, similar to the bell-shaped curve.
Does anybody recognize my fault?