Accuracy of the Markov chain level ratio solution compared to the ETLA and Jefferies method. Panel (a) compares the RH n₂/n₁ level ratio solution to the Markov chain solution. Panel (b) compares the absolute relative error of the ETLA, Jefferies, and Markov method against the RH solution. Panel (c) shows the indirect transition probabilities numerically calculated with the Jefferies ($q_{i2,1}^{\mathrm{J}}$) and Markov method ($q_{i2,1}^{{\mathrm{M}}_{\mathrm{num}}}$) for the n₂/n₁ level ratio. Panel (d) shows the analytical indirect transition probabilities from the Markov method ($q_{i2,1}^{{\mathrm{M}}_{\mathrm{ana}}}$) against Jefferies ($q_{i2,1}^{\mathrm{J}}$).