EFFECT OF SAMPLE SIZE ON IDENTIFICATION OF A JOINT PROBABILITY DISTRIBUTION UNDERLYING CORRELATED GEOTECHNICAL PARAMETERS

This paper aims to study the effect of sample size on identification of a joint probability distribution which underlies multiple correlated geotechnical parameters. First, a method for constructing the joint probability density function (PDF) of correlated geotechnical parameters using copulas is introduced. Then, a Monte Carlo-based procedure is proposed to simulate the variation of the Akaike Information Criterion (AIC) values associated with the fitted margins and copulas. The identification accuracy is defined as the probability of correct identification of the true margins and copulas. Finally, the proposed Monte Carlo-based procedure is presented to demonstrate the effect of sample size on the identification accuracy. The results indicate that the AIC values associated with the fitted margins and copulas derived from the geotechnical parameters with a small sample size show large scatter. The sample size has a significant effect on the identification accuracy of the true margins and copulas underlying correlated geotechnical parameters. The probability of correct identification of the true margins and copulas increases with increasing sample size. The coefficient of variation (COV) of geotechnical parameters has a smaller influence on the identification accuracy of the true margins, whereas the correlation coefficient between geotechnical parameters has a larger influence on the identification accuracy of the true copulas. Generally, the correct identification of the true copulas is much more demanding in data than that of the true margins. It is recommended that as much data should be collected for geotechnical parameters as possible in order to obtain high accuracy in the identified margins and copulas.