# Tagged Questions

Moments are summaries of random variables' characteristics (e.g., location, scale).

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### What's so 'moment' about 'moments' of a probability distribution?

I KNOW what moments are and how to calculate them and how to use the moment generating function for getting higher order moments. Yes, I know the math. Now that I need to get my statistics knowledge ...
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### 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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### Intuition for higher moments in circular statistics

In circular statistics, the expectation value of a random variable $Z$ with values on the circle $S$ is defined as $$m_1(Z)=\int_S z P^Z(\theta)\textrm{d}\theta$$ (see wikipedia). This is a very ...
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### Existence of the moment generating function and variance

Can a distribution with finite mean and infinite variance have a moment generating function? What about a distribution with finite mean and finite variance but infinite higher moments?
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### Error in normal approximation to a uniform sum distribution

One naive method for approximating a normal distribution is to add together perhaps $100$ IID random variables uniformly distributed on $[0,1]$, then recenter and rescale, relying on the Central Limit ...
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### Approximating $Pr[n \leq X \leq m]$ for a discrete distribution

What's the best way to approximate $Pr[n \leq X \leq m]$ for two given integers $m,n$ when you know the mean $\mu$, variance $\sigma^2$, skewness $\gamma_1$ and excess kurtosis $\gamma_2$ of a ...
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### A transform to change skew without affecting kurtosis?

I am curious if there is a transform which alters the skew of a random variable without affecting the kurtosis. This would be analogous to how an affine transform of a RV affects the mean and ...
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### Higher Moments of an Unknown Density Function

Given a R.V $X$ and that $\ E(X) = 0$ and $\ E(X^2) = \sigma^2$. Is there anyway to compute $\ E(X^3)$ without knowing the density function of $X$?
### In finding the moment generating function why do we multiply by $e^{tx}$ for each pmf term?
The moment generating function that is associated with the discrete random variable $X$ and pmf $f(x)$ is defined as: $$M(t) = E\left[e^{tX}\right] = \sum_{x \in S} e^{tx} f(x).$$ Where does this ...