# What is Mle: Definition and 25 Discussions

The Peigné-Canet-Schneider mle 1897 gun carriage was a railway gun carriage designed and built during the late 1800s. Two types of guns were mounted on these carriages and both the French Army and US Army used them during World War I. They were retired soon after World War I.

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1. ### I Why is the Maximum Likelihood Function a product?

Why is the Maximum Likelihood function a product? Explanations of how the Maximum Likelihood function is constructed usually just mention that events are independent and so the probability of several such events is just the product of the separate probabilities. I get the logic w.r.t...
2. ### MLE of Bivariate Vector Random Variable: Proof & Explanation

Homework Statement Consider the bivariate vector random variable ##(X,Y)^T## which has the probability density function $$f_{X,Y}(x,y) = \theta xe^{-x(y+\theta)}, \quad x\geq 0, y\geq 0 \; \; \text{and} \; \; \theta > 0.$$ I have shown that the marginal distribution of ##X## is ##f_X(x|\theta)...
3. ### Stuck on obtaining a closed form for parameter using MLE

Homework Statement We have a Markov Random Field with the log likelihood as such:  l(\theta) = \sum\limits_{i=1}^L \log p(x^{(i)}|\theta) = \sum\limits_{i=1}^L \left( \sum\limits_{s \in V} \theta_{s} x_{s}^{(i)} - \log \sum\limits_{x} \exp \left\lbrace \sum\limits_{s \in V} \theta_{s} x_{s}...
4. ### Maximum Likelihood and Fisher Information

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...
5. ### Find MLE of θ: Maximizing Likelihood fxn

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...
6. ### MLE estimator for mean always equal to the mean?

Suppose you have a distribution ##p(x, \mu)##. You take a sample of n points ## (x_{1}...x_{n})## from independent and identical distributions of ##p(x, \mu)##. The maximum likelihood estimator (MLE) for the mean ## \mu ## is the value of ## \mu ## that maximizes the joint distribution ##...
7. ### Fitting distribution to histogram with low number of counts

I have one dimensional binned data that has a peak to which I need to fit a distribution, such as Gaussian or Lorentzian, that is described with four parameters, height, width, centroid position and the background. The problem is that the counts per bin are low and the peak is only 5-6 bins wide...
8. ### Stats - mle poisson distribution -- quick question

This is probably a stupid question , but, It's easy enough to show that the mle of a poission distribution is ## \bar{x}##: ## \hat{ \lambda}= \bar{x} ## But,I'm then looking at the generalized ratio test section of my book, multinomial, it esitmates ## \lambda ## for some data by ## \sum...
9. ### Find a general formula for the MLE for p

An experiment consists of giving a sequences of patients a risky treatment until two have died, and then recording N, the number who survived. If p is the proportion killed by the treatment, then the distribution of N is: P(N=n)=((n+1)(1-p)^n)p^2 Find a general formula for the MLE for...
10. ### Can I omit using an indicator function when estimating an MLE?

When looking for a maximum likelihood estimator for the Uniform distribution I noticed that a common method is to use an indicator function. My initial understanding is that the reason for that is for taking into account the region of ℝ that x produces - or not - a non-zero probability. If I...
11. ### MHB MLE and sufficient statistic

Hi! I was wondering In my note we've a Corollary saying: If T is sufficient for \Theta, the maximum likelihood estimate is a function of T. where T is T(X_1,X_2,...X_n) and X is given by f(x|\Theta) I was wondering, isn't every Maximum likelihood estimator a sufficient statistic?Thanks for...
12. ### MLE of Poisson Dist: Find \lambda^2+1

Homework Statement Let X_1,...,X_n be a random sample from a poisson distribution with mean \lambda Find the MLE of \lambda^2 + 1 Homework Equations The Attempt at a Solution I found \hat{\lambda}=\bar{x} Can I just square it and add 1 and solve for lambda hat? If not I have no idea...
13. ### Finding the mle for the gamma distribution

So if the parameter \theta is alpha... L(\theta) = \frac{1}{\Gamma(\theta)\beta^{\theta}} x^{\theta-1} e^{-x/\beta} Now I take the natural log of that... ln(L(\theta)) = ln(\frac{1}{(1-\theta)!}) + ln(\frac{1}{\beta^{\theta}}) + ln(x^{\theta-1}) + ln(e^{-x/\beta}) Now I want to...
14. ### MLE for Uniform(-A,A) - exam today

So my prof. has not replied to my e-mail, so I was wondering if someone here can help me understand why the MLE for a random variable X~Unif(-θ,θ) is max|Xi|. Attached is the problem as well as my attempt for the solution. Here is my thought process: Upon sketching the graph, I thought the...
15. ### MLE of P(X<2) - Exponential distribution

Homework Statement Find the MLE of θ = P (X≤ 2) in a random sample of size n selected from an exponential distribution EXP(λ) Homework Equations f(x, λ) = λ e^(-λx) F(x, λ) = 1 - e^(-λx) The Attempt at a Solution I know how to find the MLE of the mean of an exponential...
16. ### MLE of Bernoulli trials

Homework Statement Two independent bernoulli trials resulted in one failure and one success. What is the MLE of the probability of success θ is it is know that θ is at most 1/4 Homework Equations f(x,θ) = θx (1-θ)1-x The Attempt at a Solution Now, I know how to find the likelihood...
17. ### Poisson MLE and Limiting Distribution

Homework Statement Let yi denote the number of times individual i buys tobacco in a given month. Suppose a random sample of N individuals is available, for which we observe values 0,1,2,... for yi. Let xi be an observed characterisitc of these individuals (for example, gender). If we...
18. ### MLE is biased: are there other estimation methods?

hi all, i would appreciate any help you can offer for the following problem. consider coordinates x_1, x_2 in the plane for which ||x_1-x_2||=d. suppose that this pair of coordinates can be measured independently, and that the measurements are 2D normally distributed with means x_1, x_2 and...
19. ### Stats: mle with two parameters

Homework Statement in a genetics situation, we have two variables, x1 and x2, such that both x1 and x2 >0, and x1+x2<1. we have: p1 = x12 p2 = x22 p3 = (1-x1-x2)2 p4 = 2x1x2 p5 = 2x1(1-x1-x2) p6 = 2x2(1-x1-x2) find the mles for x1 and x2. Homework Equations the answer (from the...
20. ### MLE, Uniform Distribution, missing data

I would like to determine the MLE for k in U(0,k) where U is the uniform pdf constant on the interval [0,k] and zero elsewhere. I would like this estimate in the case of missing data. To be specific, what is the MLE for k given the three draws X={1,3,*} where * is unknown.
21. ### Determining Bias of MLE of k in Poisson RP

Poisson RP: MLE of "k" P(n,tau) = [ [ (k*tau)^n ] / n! ] * exp(-k*tau) Parameter k is the process of an unknown non random variable that I want to estimate. I have determined that k^ML = [1 / (n*tau) ] sigma (xi) I believe this is correct... How do I determine if K^ML is biased?
22. ### Finding the MLE of a Poisson Distribution

Homework Statement Suppose that X has a poisson distribution with parameter \lambda . Given a random sample of n observations, find the MLE of \lambda , \hat{\lambda} . Homework Equations The MLE can be found by \Sigma^{n}_{i=1} \frac{e^{- \lambda} \lambda^{x_{i}}}{x_{i}!} = e^{-...
23. ### Find MLE for f(y/x) = (x + 1)y^x, 0 < y < 1 and x > -1

This is my question: Find the Maximum Likelihood Estimator for f(y / x) = (x + 1)y^x, 0 < y < 1 and x > -1 OR 0, elsewhere. I think this is how you get started, but I get confused. I'm not sure how to continue. The likelihood function defined as the joint density of Y1, Y2, ..., Yn...
24. ### Estimating Chip Failure Time: Geometric MLE

Homework Statement time till first failure of a chip is to be estimated. 3 such chips were tested, they worked for 30, 34, 33 days without failure. Find MLE of the parameter. The Attempt at a Solution first i want to confirm this: is this geometric distribution?
25. ### Finding the Maximum Likelihood Estimate for Theta in a Random Sample of Size 8.

I have a big test coming up, regarding estimators, but I just can't figure out the basics of maximum likilieehood. so given this example, is this right? p(k;theta) = theta^k * (1 - theta)^(1 - k), k = 0 1, and 0 < theta < 1. so it's just the product of the function, and I get...