Statistics textbooks covering moments/cumulants

In summary, the conversation discusses the concept of moment and cumulant spectra in time series analysis from a statistical perspective. The individual seeking resources and texts to further their understanding of this topic due to their limited background in statistics. Suggested resources include Kendall and Stewart's The Advanced Theory of Statistics Vol1, Random Processes by Shanmugan and Breiphol, and Probability, Random Variables and Stochastic Processes by Athanasios Papoulis. Alternatively, the individual also mentions having some familiarity with the topic based on their experiences with Random Data by Bendat and Piersol.
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boneh3ad
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I've been looking into time series analysis from a statistical perspective (looking to expand my bag of tools in analyzing experimental data) and I repeatedly run into the concept of moment and cumulant spectra. The problem is that my undergraduate course on statistics back in the day essentially never covered cumulants and only barely touched moments, and so my background is insufficient to grasp some of the richer texts on this subject.

Does anyone have any suggested resources/texts that cover this topic?

FWIW, my background is PhD-level engineering.
 
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  • #2
Kendall and Stewart's The Advanced Theory of Statistics Vol1 comes to mind but it might be a difficult place to start. Have you any experience with Random Processes? If not, I'd suggest Random Signals by Shanmugan and Breiphol.
 
  • #3
If you are an engineer, then the following book is the standard:
Probability, Random Variables and Stochastic Processes by Athanasios Papoulis.
 
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I have a little bit of familiarity with the topic based on experiences with Random Data by Bendat and Piersol.
 

Related to Statistics textbooks covering moments/cumulants

1. What are moments and cumulants in statistics?

Moments and cumulants are statistical measures that describe the shape, location, and variability of a distribution. Moments are used to calculate the center and spread of a distribution, while cumulants are used to describe the skewness and kurtosis of a distribution.

2. Why are moments and cumulants important in statistics?

Moments and cumulants provide useful information about a distribution, such as its shape and variability, which can be used to make inferences and draw conclusions about a population. They also serve as the basis for many statistical methods and tests.

3. How are moments and cumulants calculated?

Moments are calculated by taking the weighted average of a distribution's data points, with the weights being the probabilities of each data point. Cumulants are calculated from the moments using mathematical formulas.

4. What is the difference between moments and cumulants?

The main difference between moments and cumulants is that moments are affected by the shape and location of a distribution, while cumulants are affected by the shape, location, and variability of a distribution. Moments are also used to calculate cumulants.

5. Can moments and cumulants be used to compare distributions?

Yes, moments and cumulants can be used to compare distributions. By comparing the moments and cumulants of two or more distributions, we can determine if they have similar shapes, locations, and variabilities. This can help us make conclusions about the populations from which the distributions were sampled.

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