Toy model illustrating how peculiar velocities impact the observed redshift z_obs and the observed distance moduli μ_obs. Radial peculiar velocities are randomly drawn from a Gaussian distribution with σ_vp = 300 km s⁻¹. The color of each point indicates the value of its radial peculiar velocities v_p. The effect on the x-axis is of first order on v_p while the effect on the y-axis is of second order.