Indian Journal of Science and Technology

Abstract

Often, the exact density of a statistics is not available and one relies on the approximations. It is well known that Edgeworth expansions are used to approximate a probability distribution in terms of it’s first four moments of spacing statistics for small to moderate as well as large sample sizes. There is a huge literature available in which different authors analyzed statistics based on uniform spacing. Many authors established the Edgeworth expansion for sum of functions of uniform spacing. Let Sn represent the area of a convex polygon with vertices on a circle. We represent Sn as sum of sine function of uniform spacing that allow us to use the well–known results of uniform spacing. By using the famous conditions cited in the text, the Edgeworth expansion for the random variable Sn is established. The result proved in this paper can be considered as an improvement in the Central Limit Theorem for the above mentioned random variable.
Keywords: Asymptotic Normality, Edgeworth Expansion, IID Random Vectors, Random Variables, Uniform Spacing