Moment-Based Density Approximation Algorithm for Symmetric Distributions

Title & Authors
Moment-Based Density Approximation Algorithm for Symmetric Distributions
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
1.
Numerical Comparisons for the Null Distribution of the Bagai Statistic,;

Communications for Statistical Applications and Methods, 2012. vol.19. 2, pp.267-276
1.
Numerical Comparisons for the Null Distribution of the Bagai Statistic, Communications for Statistical Applications and Methods, 2012, 19, 2, 267
References
1.
Daniels, H. E. (1954). Saddlepoint approximations in statistics. The Annals of Mathematical Statistics, 25, 631-650

2.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Voll. 2nd ed., John Wiley & Sons, New York

3.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, Vol 2. 2nd ed., John Wiley & Sons, New York

4.
Joiner, B. L. and Rosenblatt, J. R. (1971). Some properties of the range in samples from Tukey's symmetric Lambda distributions. Journal of the American Statistical Association, 66, 394-399

5.
Jones, M. C. and Pewsey, A. (2005). A family of symmetric distributions on the circle. Journal of the American Statistical Association, 100, 1422-1428

6.
Ha, H-T. and Provost, S. B. (2007). A viable alternative to resorting to statistical tables. Communication is Statistics: Simulation and Computation, 36, 1-17

7.
Provost, S. B. (2005). Moment-based density approximants. The Mathematica Journal, 9, 727-756

8.
Rothman, E. D. and Woodroofe, M. (1972). A Cramer von-Mises type statistic for testing symmetry. The Annals of Mathematical Statistics, 43, 2035-2038