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An ordinary linear model -- which uses the normal distribution -- is just one GLM used for one purpose; other purposes suggest other distributions. Not all generalised linear models (GLMs) use an exponential distribution. Terminology is also confusing: "Exponential distribution" in the context of a statement like 'Generalised Linear Models use ...


3

In the original ABC version (Tavaré et al., 1999), the (dichotomous) probability of acceptance of a simulation $x(\theta)$ from $p(\cdot|\theta)$ (and hence of the parameter value $\theta$) is $$\mathbb I_{|x_\text{obs}-x(\theta)|<\epsilon}\in\{0,1\}$$ It is a natural generalisation (Fearnhead and Prangle, 2010) to consider a smoother function of the ...


3

The answer is no. You must have that $\int K_h(u)\mathrm{d}u = 1$, but that doesn't mean that $K_h(u) \leq 1$. The same applies to pdfs: a pdf $f$ can take values bigger than $1$, but it's integral $\int_a^b f(x)\mathrm{d}x = P(a \leq X \leq b)$ must be always less than $1$. You can think of the uniform distribution centered at $0$ with support $(-\epsilon, \...


2

Per Wikipedia: If $X\sim\chi^{2}(\nu)$ and $c>0$, then $cX\sim\Gamma(k = \nu/2, \theta = 2c)$. Here, $\Gamma$ denotes the gamma distribution with $k$ and $\theta$ being the shape and scale, respectively. In your case, we have $2X\sim\Gamma(3/2, 4)$.


2

When you have a small number of clusters then it may make sense to fit fixed effects for the cluster IDs. Since you have repeated measures (in countries) this needs to be accounted for and in a mixed effects or multilevel framework we usually fit random intercepts for this. There is no requirement for the dependent variables to have, or not have, any ...


2

For somebody with a strong math background like you, not intimidated by matrix algebra, I'd recommend Julian Faraway's 2 books: 1. Linear Models with R and 2. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Alternatively, in place of Faraway's second book, you could use Agresti's Categorical Data ...


2

Of the top of my head: Introduction to econometrics with R - covers basic econometrics with direct examples/applications in R (freely available online) Elements of statistical learning - the go-to statistical learning book, covers almost all model types, coupled with the solutions manual (freely available online) Introduction to Time Series - Brockwell & ...


1

This is an instance of a binomial distribution. Specifically, say $p=0.13$. Then, each person in your sample has probability $p$ of being left handed, and $1-p$ of not being so. Say $k=12,\ n=13$. Then, the probability of $k$ people out of $n$ being left handed is $ p^k (1-p)^{n-k} \binom {n}{k} $, where $\binom {n}{k} = \frac{n!}{k!(n-k)!} $ . Quoting ...


1

There is not sufficient information in your question for a responsible answer. Indeed, in view of @whuber's Comment you may not have sufficient information without further research. Therefore the following explores a tentative scenario with speculative Poisson rates, and is not intended as an answer to your question. Perhaps it will provide useful ...


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