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Results of the statistical analysis of the electrical breakdown time delay for neon-filled tube at 6.5 mbar with and without γ and ultraviolet (UV) irradiation are presented in this paper. Experimental distributions of the breakdown time delay are established on the basis of 1000 successive and independent measurements for different exposition dose rates of γ-irradiation, and UV illumination with known spectrum. Obtained experimental density distributions are modeled with convolution-based model, proposing two independent random variables with exponential and Gaussian distribution, respectively. The tendency of the breakdown time delay distribution to change shape from the exponential-like to the Gaussian-like is found by increasing the exposition rate of the γ irradiation. In addition, the characteristic strong reduction of the time delay is identified in the tube under the UV illumination.