Maximum likelihood Definition and 64 Threads

Homework Statement Let Y1<Y2<...<Yn be the order statistics of a random sample from a distribution with pdf f(x; \theta) = 1, \theta - 0.5 < x < \theta + 0.5. Show that every statistic u(X1,X2,...,Xn) such that Y_n - 0.5<u(X_1,X_2,...,X_n)<Y_1 + 0.5 is a mle of theta. In particular (4Y_1 +...

Homework Statement Suppose X1...Xn are iid and have PDF f(x; \theta) = \frac{1}{\theta} e^{\frac{-x}{\theta}} \ \ \ 0<x<\infty Find the MLE of P(X<2). Homework Equations The Attempt at a Solution I know the MLE of theta is \overline{X} so would P(X<2) = 1 -...

L(x_1,...,x_n;p)=\Pi_{i=1}^{n}(\stackrel{n}{x_i}) p^{x_i}(1-p)^{n-x_i} Correct so far? The solution tells me to skip the \Pi: L(x_1,...,x_n;p)=(\stackrel{n}{x}) p^{x}(1-p)^{n-x} This is contradictory to all the examples in my book. Why?

L(x_1,x_2,...,x_n;\theta)=\Pi _{i=1}^n (\frac{\theta}{2})^x (1-\frac{\theta}{2})^{1-x} = (\frac{\theta}{2})^{\Sigma^n_{i=1}x_i}(1-frac{\theta}{2})^{n-\Sigma^n_{i=1}x_i} Correct so far if f(x) = (\frac{\theta}{2})^x (1-\frac{\theta}{2})^{1-x} ? lnL(x_1,x_2,...,x_n;\theta) =...

Homework Statement pdf: f(x)=ax^(a-1) ; 0<x<1, a>0 estimate a by maximum likelihood Homework Equations let L be maximum likelihood L=(a(x[1])^(a-1))(a(x[2])^(a-1))...(a(x[n])^(a-1)) The Attempt at a Solution Im trying to make this into a nicer expression: L=a^n... (now I am...

Hi, I'm posting this in this particular forum because, though this's a statistics question, my application is in high energy. My question is regarding a problem in Bevington's book (Data Reduction and Error Analysis..., Page 193, Ex. 10.1), but I'll give a general description here... Say...

Homework Statement Let's have random value X defined by its density function: f(x; \beta) = \beta^2x \mbox{e}^{-\beta x} where \beta > 0 for x > 0 and f(x) = 0 otherwise. Expected value of X is EX = \frac{2}{\beta} and variance is \mbox{var } X = \frac{2}{\beta^2}. Next...

Homework Statement Suppose X has a Poisson distribution with parameter lambda. Given a random sample of n observations, Find the MLE of lambda, and hat lambda. Find the expected value and variance of hat lambda. Show that hat lambda is a consistent estimator of lambda. Homework...

in need of help for how to do this question given probability mass function: x 1 2 3 4 p(x) 1/4(θ+2) 1/4(θ) 1/4(1-θ) 1/4(1-θ) Marbles 1=green 2=blue 3=red 4=white For 3839 randomly picked marbles green=1997 blue=32 red=906...

http://en.wikipedia.org/wiki/Maximum_likelihood What exactly does the "arg" here mean? It seems to be an unnecessary - the max L(\theta) seems to be sufficient enough. Or am I missing something? \widehat{\theta} = \underset{\theta}{\operatorname{arg\ max}}\ \mathcal{L}(\theta).

Hi, I'm taking a basic course in statistical methods, and we recently learned of maximum likelihood estimation. We defined the likelihood as a function of some parameter 'a', and found the estimator of 'a' by requiring a maximum likelihood with respect to it. As an example, we took the...

Can anyoe help with likelihood estimtor problems? :cry:

How do I estimate the standart deviation for the mean average of an poisson-distribution ? The mean average was estimated with the maximum-likelihood method by graphing the likelihood in dependence of the mean average, then just reading off the value for which the likelihood became maximal. Up...

Maximum likelihood estimator... ok, I'm stil a bit lost...so tell me if this is right: f_y(y;\theta) = \frac{2y}{\theta^2}, for 0 < y < \theta find the MLE estimator for theta. L(\theta) = 2yn\theta^{-2 \sum_1^n y_i . is this even right to begin with? then take the natural...