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Statistics Chapter 1
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- 1Maximum LikelihoodL(theta1, ....., thetan ; y1, ...., yn) =
Product[1-n] f(yi ; theta i) - 2Log Likelihoodl (theta 1, ..., theta n ; y1, ...., yn) =
SUM[1 -n] log [f(yi;theta i)] - 3Convergence in distn of random variablesLet Xn[1-infinity] be a sequence of random variables such that Xn has cdf Fn. Let X be a random variable with cdf F.
Say Xn converges in distribution to X as n -> infinity, or
Xn -(D)-> X
if lim Fn(x) = F(x) at every point x where F is cts. - 4Central Limit TheoremLet Xn[1-infinity] be a sequence of independent and identically distributed random variables such that
E(Xn)=0
Var(X^2)=sigma^2
Let Sn = SUM[1-n]Xi and Z~N(0,1).
Then Sn/(sigma/sqrt n) -(D)-> Z as n->infinity - 5Why is CLT useful?The CLT is useful for approximating the distribution of sums of
i.i.d random variables. However, it is not possible to give a concise
statement about how good the approximation is. A general
guideline is that the number of terms in the sum must be “large”.
Usually, > 30
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- BSc (Statistics II) Maths Fichas sobre Statistics Chapter 1, creado por joe.clay11 el 20/07/2013.
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