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### Generic sum of Gamma random variables

I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
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### Do third order asymptotics exist?

Most asymptotic results in statistics prove that as $n \rightarrow \infty$ an estimator (such as the MLE) converges to a normal distribution based on a second-order taylor expansion of the likelihood ...
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### Real life uses of Moment generating functions

In most basic probability theory courses your told moment generating functions (m.g.f) are useful for calculating the moments of a random variable. In particular the expectation and variance. Now in ...
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### Series expansion of a density function

Here's something I've wondered about for a while, but haven't been able to discover the correct terminology. Say you have a relatively complicated density function that you suspect might have a close ...
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### Why Use the Cornish-Fisher Expansion Instead of Sample Quantile?

The Cornish-Fisher Expansion provides a way to estimate the quantiles of a distribution based on moments. (In this sense, I see it as a complement to the Edgeworth Expansion, which gives an estimate ...
803 views

### Finding the distribution of iid variables X, Y given distribution of X-Y

Say I know the distribution of $X-Y$, but I do not know the distributino of $X$ (or $Y$), but I know that they are statistically independent, and I know they have the same distribution. Is the problem ...
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### Elementary approach to higher order asymptotics

I am trying to understand “higher order asymptotics”. I find several texts on Likelihood asymptotics, nothing’s easy to read... if you have any nice pointers on this direction, I’ll be interested; ...
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### Literature on nonparametric density estimation

I am about to write my bachelor thesis about non-parametric density estimation, especially kernel density estimators and their application in classification. As I am quite new to looking for academic ...
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### How to find the distribution of the weighted sum of independent Bernoulli random variables for positive non-integer weights

How do I find the distribution of the weighted sum of independent Bernoulli random variables if the weights are non-negative real numbers? I have N number of independent Bernoulli distributed random ...
328 views

### Sum of linear combination of product of exponentials is exponential

This problem has arisen in my research: suppose that $V_i \sim \text{ED}$ are iid exponential distributions (ED) with mean $1$ and let $\lambda$ be a nonnegative number. Is it true that  \sum_{k=0}^...