Questions tagged [partial-moments]

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2
votes
2answers
587 views

What should the integral of a CDF be called?

This is strictly a nomenclature question. I have no particular problem finding double integrals of the type $\int\int\text{pdf}(y) \, d y \,d x$, and I find them quite useful. Whereas we have a good ...
2
votes
2answers
72 views

Is there a phrase for to describe $xf(x)$ where $f(\cdot)$ is the probability mass function?

We know that $\mathbb{E}[X] = \sum_x xf_{X}(x)$ where $f_X(\cdot)$ is the probability mass function. Is there any phrase that we use to describe $\sum_{x\le a} xf_X(x)$, or is there any phrase that we ...
3
votes
0answers
63 views

Measures of central tendency for right-skewed size distributions

Suppose we are looking at a right-skewed size distribution such as the distributions of income, casualty losses, or flood sizes, and we want to look at some alternative measures to jointly represent ...
1
vote
0answers
41 views

Partial quantile moments?

The integral from 0 to x* of x to the n times pdf(x) is usually called the nth partial moment function. Does the corresponding integral from 0 to y* of y to the n of the quantile density function, qdf(...
5
votes
2answers
9k views

Integral of a CDF

I'm solving a problem where I've this 'expectation': $$ \int_{0}^y x\cdot f(x) dx $$ where $f(x)$ is a PDF with support on $[0, z]$, with $z>y$. Is there a way to rewrite it without the integral ...
46
votes
3answers
7k views

How does saddlepoint approximation work?

How does saddlepoint approximation work? What sort of problem is it good for? (Feel free to use a particular example or examples by way of illustration) Are there any drawbacks, difficulties, things ...
15
votes
1answer
887 views

When would we use tantiles and the medial, rather than quantiles and the median?

I can't find definitions for either tantile or medial on Wikipedia or Wolfram Mathworld, but the following explanation is given in Bílková, D. and Mala, I. (2012), "Application of the L-moment method ...
41
votes
4answers
31k views

What is the difference between finite and infinite variance

What is the difference between finite and infinite variance ? My stats knowledge is rather basic; Wikipedia / Google wasn't much help here.
20
votes
3answers
5k views

Moments of a distribution - any use for partial or higher moments?

It is usual to use second, third and fourth moments of a distribution to describe certain properties. Do partial moments or moments higher than the fourth describe any useful properties of a ...