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A procedure for computation of the nonlinear refractive index of a gaseous medium from the intensity dependence of the ionization rate is reported. The ionization rate is calculated from Keldysh theory via a Kramers-Kronig transform. Peremolov-Popov-Terent'ev (PPT) theory is analyzed in the perturbative limit of multiphoton ionization for a completely analytical expression for the nonlinear refractive index. The method requires knowledge of only the particle density and the ionization energy of the gas. Example calculations are performed for the inert gases and compared to experimental data and atomic model calculations for the hyperpolarizability of the respective media. Excellent agreement between reference data and the computed values derived from the Kramers-Kronig transform is found in the visible and infrared spectral range. Additionally, higher-order nonlinear refraction is discussed.