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gregorygundersen.com | ||
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statisticaloddsandends.wordpress.com
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| | | | | In this previous post, we defined Value at Risk (VaR): given a time horizon $latex T$ and a level $latex \alpha$, the VaR of an investment at level $latex \alpha$ over time horizon $latex T$ is a number or percentage X such that Over the time horizon $latex T$, the probability that the loss on... | |
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nelari.us
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| | | | | In inverse transform sampling, the inverse cumulative distribution function is used to generate random numbers in a given distribution. But why does this work? And how can you use it to generate random numbers in a given distribution by drawing random numbers from any arbitrary distribution? | |
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jaketae.github.io
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| | | | | "I think that's very unlikely." "No, you're probably right." | |
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djalil.chafai.net
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| | | Let $X$ be an $n\times n$ complex matrix. The eigenvalues $\lambda_1(X), \ldots, \lambda_n(X)$ of $X$ are the roots in $\mathbb{C}$ of its characteristic polynomial. We label them in such a way that $\displaystyle |\lambda_1(X)|\geq\cdots\geq|\lambda_n(X)|$ with growing phases. The spectral radius of $X$ is $\rho(X):=|\lambda_1(X)|$. The singular values $\displaystyle s_1(X)\geq\cdots\geq s_n(X)$ of $X$ are the eigenvalues of the positive semi-definite Hermitian... | ||
