# Probability Theory: Cramer Transform Issue and deviation probabilities theory.

Let $\xi$ be random variable with probability distribution $F_\xi$.

Let $\tilde\xi$ be random variable with probability distribution $\tilde F_\xi$

$I_{\xi}^t(x) = \int \limits_{-\infty}^x e^{ts}dF_\xi(ds)$

$\tilde F_\xi (x) = \frac{I_{\xi}^t(x)}{I_{\xi}^t(+\infty)}$

Then, we can say, that we use Cramer transform with $\xi$ variable.

Ok, Cramer transform we can use with all distributions.

But in deviation probabilities theory Cramer transform uses very often.

Question, related to deviation probabilities theory: Can anybody explain this tip: Is it needed to approximate discrete probability distribution with continuous probability distributions? For which reason?

Thank you!

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What is the question? – Did Mar 12 '13 at 22:27
Is it needed to approximate... – gaussblurinc Mar 13 '13 at 6:00
Then the answer is NO, there is no direct relationship between LD theory and the approximation of discrete probability distribution by continuous probability distributions. What makes you think there could be some? – Did Mar 13 '13 at 6:31