Mechanical structural vibration is traditionally addressed using the system identification method, which uses a random vibration response. In this study, we propose an identification method based on a probability density function. The probability density function has a shape that is determined by system parameters, such as the spring constant (linear or nonlinear), damping constant, and diffusion coefficient of the input white noise. These characteristics are not directly related to the frequency spectrum. Therefore, a probability density function-based method is expected to be applicable to systems with low S/N ratios. An accuracy comparison was conducted in this study. As a result, when the estimation error rate exceeded 1%, the nonlinear model reduced the error rates of both the linear and nonlinear spring constants. On the contrary, the estimation results based on the linear model revealed a high-accuracy region in the low \(\mu /k\) values. To obtain the guideline for PDF model selectivity, we introduced the average error rate in spring constant estimation results. The optimized ratio of \(\mu /k\) was observed in the region between 0.5% and 1%. Therefore, in a weakly nonlinear system (i.e., a ratio of \(\mu /k\) less than around 1%), the linear spring constant can be estimated using both linear and nonlinear models.