HI

[anvar]

Here we need to estimate p_i, q_i, and β.

Thank you,

> Min∑_(i=1)^n▒∑_(t=1)^l▒[s_i (t)-min[s ̂_i (t)×α_t×exp(g_t ),C_i
> (t) ] ]^2
> subject to
> s_i (t)=f_i (t)[S_i+f_(i-1) (t)[S_(i-1)+f_(i-2) (t)[S_(i-2)+⋯f_2 (t)
> [S_2+f_1 (t) S_1 ]…] ] ][1-f_(i+1) (t)]
> f_i (t)=F_i (t)-F_i (t-1)
> F_i (t)=(((1-e^(-(X_i (t)-X_i (0) )(p_i+q_i ) )))/(((q_i⁄p_i ) e^(-
> (X_i (t)-X_i (0) )(p_i+q_i ) )+1)), if t≥τ_i     and F_i (t)=0  if
> t<τ_i
> X_i (t)=(t-τ_i+1)+ln(〖pr〗_i (t)/〖pr〗_i (0))β
> α_t≥0,       g_t=const
> 0<p_i<1,               0<q_i<1
> S_i>0,
> ∀i=1,2,…,n
> Where
> s ̂_i (t)=p_i S_i  +(q_i-p_i ) s_i (t-1)-(q_i/S_i ) [s_i (t-1) ]^2,
> S_i=μ_i (t)M_i