Moment-Based Density Approximation Algorithm for Symmetric Distributions

- Journal title : Communications for Statistical Applications and Methods
- Volume 14, Issue 3, 2007, pp.583-592
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2007.14.3.583

Title & Authors

Moment-Based Density Approximation Algorithm for Symmetric Distributions

Ha, Hyung-Tae;

Ha, Hyung-Tae;

Abstract

Given the moments of a symmetric random variable, its density and distribution functions can be accurately approximated by making use of the algorithm proposed in this paper. This algorithm is specially designed for approximating symmetric distributions and comprises of four phases. This approach is essentially based on the transformation of variable technique and moment-based density approximants expressed in terms of the product of an appropriate initial approximant and a polynomial adjustment. Probabilistic quantities such as percentage points and percentiles can also be accurately determined from approximation of the corresponding distribution functions. This algorithm is not only conceptually simple but also easy to implement. As illustrated by the first two numerical examples, the density functions so obtained are in good agreement with the exact values. Moreover, the proposed approximation algorithm can provide the more accurate quantities than direct approximation as shown in the last example.

Keywords

Approximation algorithm;density approximation;moments;percentage points;symmetric distributions;transformation of variables;

Language

English

Cited by

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