S-Space College of Natural Sciences (자연과학대학) Dept. of Statistics (통계학과) Theses (Master's Degree_통계학과)
Limit Distribution of Spacing on the Unit Circle
단위 원 상 스페이싱의 극한분포
- 자연과학대학 통계학과
- Issue Date
- 서울대학교 대학원
- Spacing; Uniform spacing; Dirichlet distribution; Circular statistics; Directional statistics
- 학위논문 (석사)-- 서울대학교 대학원 : 통계학과, 2017. 2. 임요한.
- Order statistics of continuous uniform random variable on unit interval are
related to several distributions. It is known that spacings, one of combina-
tions of order statistics, follow the Dirichlet distribution. It can be applied
to circular uniform random variables also with mild modication. In this
paper, we review the derivation of the joint distribution of spacings on the
unit interval and circle. Using this, we prove that the distribution of discrete
random variables from a circular arrangement that consist of two distinct
elements converges to Dirichlet distribution.