Construction and transformation of probability densities
Integrated Computer-Aided Engineering
| Hi-index | 0.00 |
We derive a general equationrelating probability densities and as special cases we the obtainGram-Charlier and Edgeworth series. This allows us to generalizethese methods and clarify a number of issues pertaining to bothprobability theory and time-frequency analysis. In particularwe show how the Gram-Charlier and Edgeworth series are relatedto the kernel method of time-frequency analysis. The approachallows us to construct densities that satisfy given constraintssuch as joint moments or conditional moments. Also, we show thatthe kernel has to be signal dependent and that to obtain a properdistribution it should be the ratio of two characteristic functions.