An Empirical Approach to the Normality of π
نویسندگان
چکیده
Using the results of several extremely large recent computations [17] we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of π. This result was used by a Poisson process model of normality of π: in this model, it is extraordinarily unlikely that π is not asymptotically normal base 16, given the normality of its initial segment.
منابع مشابه
On the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality
It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...
متن کاملSome Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling
In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...
متن کاملOn the Asymptotic Statistics of the Number of Occurrences of Multiple Permutation Patterns
We study statistical properties of the random variables Xσ(π), the number of occurrences of the pattern σ in the permutation π. We present two contrasting approaches to this problem: traditional probability theory and the “less traditional” computational approach. Through the perspective of the first one, we prove that for any pair of patterns σ and τ , the random variables Xσ and Xτ are jointl...
متن کاملAn Empirical Assessment of the Monetary Approach to Endogenous Technical Progress Theory: DSGE approach
Economis growth is one of the main factors for evaluating the performance of governments. Economic growth itself is influenced by other factors that have been addressed in growth theories. Among the factors examined in growth theories, technical progress is of particular importance due to its long-term effects on growth. In recent growth models, the technological progress considered an endogeno...
متن کاملEstablishing an Argument-Based Validity Approach for a Low-Stake Test of Collocational Behavior
Most of the validation studies conducted across varying test application contexts are usually framed within the traditional conceptualization of validity and therefore lack a comprehensive framework to focus on test score interpretations and test score use. This study aimed at developing and validating a collocational behavior test (CBT), drawing on Kane's argument-based approach to validity. F...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Experimental Mathematics
دوره 21 شماره
صفحات -
تاریخ انتشار 2012