I want to write a function in R for simulating 3 numbers of gamma procees that each process represent degradation process of a defect in a system we assume 3 gamma process {X_k(t);t>=0}, k=1,2,3 ,all of which start at random times, following a homogeneous poisson process with rate λ=1 and they are independent with respect to k. We assume X_k(t)~gamma(α_k(t),β_k) where α_k(t)is a given monotone increasing function in t and α_k(0)=0 and We assume that α_k(t)= α_k*(t^ξ_k) and α_1= α_2= α_3=1 , β_1=1, β_2=2, β_3=3. And y( t )= 0.2X_1( t )+0.7X_2 ( t ) +0.4*X_3 ( t ) represent overal degradation of the system And i want to know how to plot them
My codes in R is:
t=10
f=function(t){t^2}
y=c()
g=function(t){
for(i in 1:10){
x1=rgamma(1,f(t),1)
x2=rgamma(1,f(t),2)
x3=rgamma(1,f(t),3)
y[i]=0.2*X1+0.7*X2+0.4*X3
}
return(y)
}
g(10)
I want to know my mistakes and know whatever I should concern this point in my simulation that occurances of the defects follows poisson process And I want to know which function is useful to represent their degradation process plot. Thanks for helping