Moment-Based Density Approximation Algorithm for Symmetric Distributions
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.
- Daniels, H. E. (1954). Saddlepoint approximations in statistics. The Annals of Mathematical Statistics, 25, 631-650
- Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Voll. 2nd ed., John Wiley & Sons, New York
- Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, Vol 2. 2nd ed., John Wiley & Sons, New York
- 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
- 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
- Provost, S. B. (2005). Moment-based density approximants. The Mathematica Journal, 9, 727-756
- Jones, M. C. and Pewsey, A. (2005). A family of symmetric distributions on the circle. Journal of the American Statistical Association, 100, 1422-1428
- Rothman, E. D. and Woodroofe, M. (1972). A Cramer von-Mises type statistic for testing symmetry. The Annals of Mathematical Statistics, 43, 2035-2038
이 논문을 인용한 문헌 (1)
- 2012. "" 한국통계학회 논문집 = Communications of the Korean Statistical Society, 19(2): 267~276
원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.
NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.
- 이 논문과 함께 출판된 논문 + 더보기