The stress concentration factor, which is one of the primary input parameters for the fatigue reliability analysis of tubular joints commonly found in offshore jacket structures, shows substantial scatter that highlights the importance of accurate derivation of its governing probability function. In this article, results of 144 finite element stress analyses, validated using experimental data, were used to derive the probability density functions for the stress concentration factors in unstiffened gap tubular KT-joints under four types of out-of-plane bending moment loadings. Based on a parametric finite element study, a sample database was prepared for the maximum chord-side stress concentration factors of central and outer braces, and density histograms were generated for these samples. Nine different probability density functions were fitted to these histograms. The maximum likelihood method was used to estimate the parameters of fitted distributions. In each case, Kolmogorov-Smirnov test was applied to assess the goodness-of-fit. Finally, the inverse Gaussian model was selected as the best-fitted distribution, and after substituting the values of estimated parameters, six fully defined probability density functions were proposed for the maximum chord-side stress concentration factors of central and outer braces in unstiffened gap KT-joints under four types of out-of-plane bending loading.