Abstract: This research explored optimal match between distribution of the examinees ability and distribution of the items ' difficulty by Monte Carlo Simulate Approach. The results showed that when the distribution of the examinees ' ability were standard normal, positive skewness or negative skewness and the distribution of items ' difficulty were the same as ability distribution respectively, the indices of match, such as the expected information function value, maximum information function value and reliability were higher than the other match indices. The accuracy was also higher than the other match in estimating item difficulty, discrimination and examinees ' ability.

Key words: item response theory, expected value and maximum value of information function, optimal match