Questions tagged [partial-moments]

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6 votes
2 answers
212 views

What is the derivation for "Partial Expectation"?

On the Wikipedia page for Log-normal distribution It is written that $$E[X|X>k]Pr(X>k)=\int_{k}^{\infty}xf_{X}(x)dx$$ I know it is probably simple, but I am still wondering the derivation. Since ...
  • 658
0 votes
0 answers
36 views

Expected value of a random variable with truncation

Let $f:[0,\infty)\to \mathbb R_+$ denote the PDF of a random variable $X$ and $c>0$ a constant. I want to evaluate the following integral: $$I(c)=\int_0^\infty{\min(x,c)f(x)dx}.$$ This can be ...
  • 113
4 votes
2 answers
2k 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 ...
  • 11.9k
2 votes
2 answers
80 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 ...
  • 121
3 votes
0 answers
67 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 ...
  • 2,627
1 vote
0 answers
45 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(...
  • 2,627
7 votes
2 answers
13k 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 ...
  • 257
50 votes
3 answers
10k 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 ...
  • 264k
18 votes
1 answer
1k 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 ...
  • 21.3k
46 votes
4 answers
38k 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.
21 votes
3 answers
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 ...
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