Analytical expression for the integrated squared density partial derivative of a multivariate normal mixture distribution
| Autor: | Min-Hsiao Tsai |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Maple Applied Mathematics 05 social sciences Multivariate normal distribution engineering.material Mixture model 01 natural sciences Expression (mathematics) Numerical integration 010104 statistics & probability Modeling and Simulation 0502 economics and business engineering Applied mathematics Mixture distribution Partial derivative 0101 mathematics Statistics Probability and Uncertainty MATLAB computer 050205 econometrics computer.programming_language Mathematics |
| Zdroj: | Journal of Statistical Computation and Simulation. 88:2726-2750 |
| ISSN: | 1563-5163 0094-9655 |
| DOI: | 10.1080/00949655.2018.1485152 |
| Popis: | This paper describes the derivation of the analytical expression for the integrated squared density partial derivative (ISDPD) in a multivariate normal mixture model. The analytical expression of the ISDPD is derived for arbitrary dimensions with partial derivative orders up to four. Although the value of the ISDPD can be obtained by using the common numerical integration via mathematical software (such as Maple, Mathematica, Matlab, etc), it suffers from the limitation of computation time when the dimension or the number of mixture components of the considered multivariate normal mixture model are large. Moreover, numerical comparison indicates the benefits of speed offered by our proposed analytical expression are far superior to the numerical integration performed by Maple. With this analytical expression, the ISDPD can apace be calculated with no assistance of numerical integration. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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