Tagged Questions

3
votes
0answers
40 views

Likelihood analysis for exponential distribution

Assume a collection of independent exponential random variables $y_{1}, \ldots, y_{n}$ with means $\mu_{1}, \ldots, \mu_{n}$; where $\mu_{i} = \beta_{0}+\beta_{1}x_{i}$. How can I find the profile ...
1
vote
1answer
218 views

Hypothesis testing of normal distribution, known mean unknown variance

I've been working on review problems, and this one has me completely stumped. Let $X_1 ... X_{10}$ be a random sample from a $N(3,\sigma^2)$ distribution, where $\sigma^2$ is unknown. Using the ...
-4
votes
1answer
110 views

Maximum Likelihood Estimator (MLE)

Salmon sometimes carry a parasite anisakis simplex which they pick up when feeding on krill at sea. The number of parasites on each fish might be assumed a random variable X having a probability ...
1
vote
1answer
86 views

exponential density & bernoulli distribution

I had asked a question on Maximum Likelihood earlier. Now I have two questions that are related to this question which had: Let $x$ have an exponential density $p(x|\theta) = \theta e^{-\theta x} ...
1
vote
1answer
59 views

I am stuck with proof of MLE for Logistic regression

Hi all, I am doing a self study of logistic regression and working through the proof of the MLE; please see picture from Montgomery and Peck text. Could someone please fill in the intermediate ...
2
votes
1answer
52 views

Trouble writing likelihood

I'm having trouble writing the likelihood for a homework question: Suppose $X=Z(Y+\theta)+(1-Z)(\theta-Y)$ and $X_1, X_2, X_3 \overset{iid}{\sim} f_X(x)$ where $Z\sim \rm{Bernoulli}(0.5)$ and $Y\sim ...
1
vote
1answer
204 views

Write down the log-likelihood function for this model

Consider the regression model $$ Y_i = ax_i^3 + \epsilon_i, \hspace{1cm} i = 1,...,n$$ with $\epsilon_i \sim N(0, \sigma^2)$ and $\epsilon_i, \epsilon_j$ independent for $i \neq j$. Write ...
0
votes
1answer
71 views

maximum likelihood estimate

This problem compute to showing cource. Fie tosses of a coin with P(head)=p resulted in H,T,T,T,T. ...
0
votes
0answers
69 views

MLE of a function of a parameter

I am working on a problem where we are interested in finding the MLE for a function of two parameters. I am having problems with going about finding this. Intuitively, the idea makes sense. I am just ...
3
votes
0answers
117 views

Weird MLE Problem based on Dirichlet Function

This question was on a HW in my Statistical Theory class and I find the professor's answer and explanation to be unsatisfactory. Please give me some guidance as to why $\bar{x}$ is the MLE if this ...
0
votes
0answers
91 views

Deriving asymptotic distribution

I'm working on a question and I appreciate if you could guide me on how to approach it. Here is the question: Consider $Y_1, Y_2, \ldots, Y_n$ as iid with density $f(y;\theta)$ and assume that the ...
3
votes
0answers
155 views

Simple question Maximum Likelihood

I have the following distribution, defined for $0 < x < \theta$, its value is $0$ otherwise. $$f_\theta(x)= \frac{2x}{\theta^2} $$ Find the MLE of $\theta$ I tried: $$\prod_{i=1}^n ...
2
votes
1answer
259 views

Simple MLE Question

Let $X_1, X_2...X_n$ be iid with $f(x,\theta)=\dfrac{2x}{\theta^2}$ and $0<x\leq\theta$. Find $c$ such that $\mathbb{E}(c\hat{\theta})=\theta$ where $\hat{\theta}$ denotes MLE of $\theta$. What I ...
1
vote
1answer
215 views

Maximum likelihood estimation and the n-th order statistic

Let $X_1, ..., X_n$ be a sample of independent, identically distributed random variables, with density $$ f_{\theta}(x)=e^{ (\theta -x)}$$. $x \ge \theta$, otherwise $f_\theta = 0$ The question ...
-1
votes
1answer
124 views

Maximum likelihood estimator (Gaussian errors, known SD)

Suppose that the random variables $Y_1, ..., Y_n$, satisfy $Y_i = \beta \cdot x_i + \epsilon_i$ for $i = 1,...,n$ where $\beta$ is a constant, $x_1,...,x_n$, are constants, and ...
-1
votes
1answer
141 views

Finding the MLE of parameter $\mu$

Suppose $X_1,\ldots,X_n$ are a random sample of a continuous and strictly increasing distribution $F(x)$ with mean $\mu$. If $$ Y_i = \begin {cases} 2 & \text{if}\ X_i>\mu \\ 1 & ...
0
votes
0answers
361 views

Cramer-Rao Lower Bound Questions

I've been reviewing questions from a statistics exam of the last year. There is a question with the probability density function below $$\displaystyle f(x,\theta) = \frac 1{2\theta^3}x^2e^{-\frac ...
0
votes
1answer
96 views

Mixed Ques on Markov Chains, Kolmogrov Differential Equations, Thieles DE, MLE, Reserves [closed]

I have attached 2 documents and listed my questions below. hoop://www.mediafire.com/?9u3vc2dop16okna hoop://www.mediafire.com/?4b994pl89ljdqql (replace 'hoop' with 'http') I thought it would be ...
1
vote
2answers
557 views

Maximum likelihood and sufficient statistics

fT(t;B,C) = exp(-t/C)-exp(-t/B) / C-B where our mean is C+B and t>0. so far i have found my log likelihood functions and differentiated them as follows: dl/dB = sum[t*exp(t/C) / ...