Identification of the best-fit joint probability distribution for a small set of samples is a challenging problem. Based on the Bootstrap method, an optimum marginal distribution function and an optimum Copula function for identifying the geotechnical parameters with a small sample size are proposed. The Copula method for constructing the joint probability distribution function (PDF) for correlated geotechnical parameters is briefly introduced, and then the Akaike Information Criterion (AIC) is adopted to identify the optimum marginal distribution function and Copula function. The identification results are represented by a collection of the weight factors such that each candidate marginal distribution function and copula function become the optimum (best-fit). Four measured datasets of the hyperbolic load-settlement curve-fitting parameters of piles are used to demonstrate the validity of the proposed method. The results indicate that the sample mean, sample standard deviation and sample correlation coefficient derived from the geotechnical parameters with a small sample size are relatively scattering, leading to a higher variation in the AIC values associated with the fitted marginal distributions and Copulas. The proposed bootstrap method can effectively consider the variation of the AIC values of the fitted marginal distributions function and Copulas function. It can also account for the possibilities that each candidate marginal distribution function and Copula function become the optimum. The bootstrap method provides a general and practical tool for identifying the best-fit marginal distribution function and Copula function with a small sample size.