The purpose of this paper is to discuss the discrete probability distribution function induced from the modified bucket sorting. The distribution is related to the unique sequence called "Eulerian Numbers" proposed by Euler (1755). There are sensitive differences between a derivation process of our proposal and Eulerian numbers expressed as a number of permutation runs. Recurrence relation for the moments of the distribution is also given. The mean, variance and higher order cumulants are derived using the relation. The interesting results that the relationship among the proposed, normal and uniform distributions are shown by asymptotic expansion. The efficiency of the proposed method is illustrated through some numerical experiments.
Correlation analysis among variables are frequently used in various approaches of statistics and data mining. However, its application to the data obtained from the recent ubiquitous sensing system consisting of massive sensors is often intractable, since its computational complexity is proportional to the square number of variables. On the other hand, the strong correlations among the variables are usually sparse in various data such as small world data. In this report, we propose a novel method to efficiently estimate the correlations among massive variables under this sparseness. Its experimental evaluations show excellent performance in efficiency comparing with the direct computation of all correlation coefficients.
To understand basic elements in programming is nessesary to develop a system. But ``just an understanding'' is not enough to develop a system by oneself and there are researches that emphasize an actual experience to write a code by hands-on training to get a deep understanding. To think about the fewness of basic elements in programming there is a possibility of changing quality of comprehensions by a repeating experience of using basic elements. In this research we did a experiment to research a connection between programming experience and a development skill. The results of the experiment are following 3 points: (1) A person who programs often have a high development skill; (2) A person who dose not programs often can understand a certain algorhythm but can't implement it, even if the one had understand basic element of programming (pass a introductory and advanced class); (3) One of the difficult line for novice programmers to write a code by oneself is nesting structure with a variable operating process.