1. An information processing apparatus comprising: a memory configured to have computer readable program stored thereon; and a central processing unit (CPU) arranged to receive the program from the memory and upon execution thereof to operate as (i) a first calculation unit that calculates a probability function with highest likelihood based on data, (ii) a second calculation unit that calculates a canonical distribution in statistical physics and a parameter of the canonical distribution as a fluctuation of the data, and (iii) an estimation unit that estimates a probability function using the probability function with the highest likelihood calculated by the first calculation unit, the fluctuation calculated by the second calculation unit, and the canonical distribution, wherein when the second calculation unit calculates the fluctuation of the data, n data items are used, and Kullback-Leibler information is calculated by the probability function calculated based on (n-1) data items by the estimation unit and one of a probability function with the highest likelihood calculated based on the n data items, a Bayesian posterior probability function, and an empirical distribution function.