Chronos model's formula

Q&A
1

Cannot understand how the formula I circled was derived…Can anyone helps me? thanks![

1

2

It may be easier to see in reverse. Starting with the final formula:

  • let d_g = 0
  • p_c p_j = p_cj
  • Note that we can multiply Z by any value that is uniform over the guides without changing nu_cj. So multiply it by e^{R_c t}
  • After distributing, you should see that the identity on the third line is true if nu_cj(0)/sum_j(nu_cj(0)) = N_cj(0)/sum_j(N_cj(0))