# maximum likelihood

1. ### Maximum likelihood estimation for exponential distribution

I would like to describe some gathered data for arrival process which seems not following Poisson distribution for people finding a job. The data consists of two subpopulations (but we have only the combined results), first subpopulation where people assigned to the correct place (correct place...
2. ### MLE and vector generalized linear models

Hello and thank you very much for your time I am working to simultaneously (multivariate) regress 'A' and 'B' parameters from matched observations of predictors (I have an 'A' and 'B' for each set of predictors and all are continuous random variables). The 'A' and 'B' parameters are...
3. ### Maximum likelihood estimation of transition probabilities

Hi, I'm new to Markov chains but have been advised by a colleague to use this approach for my latest study. I have a basic understanding of the theory but I am confused by the use of maximum likelihood for estimating the transition probabilities. Why is this done and also how is it done? In my...
4. S

### parameter estimation based on observed survival probabilities

Say 100 samples have been pulled from a Normal distribution with unknown mean and variance. All I know about the results are the following: • 23 out of 100 are greater than 200 • 9 out of 100 are greater than 300 • 2 out of 100 are greater than 400 How would I find the best estimate of...
5. ### Maximum likelihood estimation and GLMs - can you help me refresh my rusty memory?

Hi all, I was wondering if you can help me refresh my rusty memory on maximum likelihood estimation. I think I remember the basic concept from my university courses in a previous life. Banal example: we want to fit a normal distribution to the observations 3,4,5, then N(4,1) is the best...
6. ### Maximum Likelihood Estimator - Geometrical Distribution

Do you know a site which gives a step by step solution of finding the MLE for Geometric Distribution? I'm thinking about something like this http://en.wikipedia.org/wiki/Exponential_distribution#Maximum_likelihood but for Geometric Distribution.
7. ### MLE for X ~ Exp(λ)

Let (X1, ... Xn) be a random sample from a random variable. Find the maximum likelihood estimator for λ. I know the answer to this but do you have a link to a step by step solution? I found sites which show all stages for finding the estimator for other distributions only.
8. ### Problem of maximum likelihood estimation of time series

Hi everyone, I have a problem of how to calculate the MLE for a given time series data set. I have read the book Statistical Method for Forecasting, there are some example of building AR model but it simply stated that the MLE are the multiple of two quantities. I have no idea on how these...
9. ### Stata: ml versus nl

I need to estimate an equation using some iterative method to optimally choose the coefficients. I won't go into the reasons that I can't use a simpler methods like OLS, GLS or instrumental variables (it's a long, sad story). My question is about weather I can expect equivalent results from...
10. ### Estimating Confidence Intevals

Hi, I have used a loglikelihood function to estimate 24 parameters. How do I construct a confidence interval given the Hessian (avaliated on the estimatives) and the gradiente(avaliated on the estimatives). Do I need both? What I saw is that, given that MLE is assymptoticaly normal I...
11. ### How do I perform a generalized estimate equation with penalized maximum likelihood...

...in SPSS? The reason I ask is that SPSS tell me I have a quasi-complete separation of my data and after some reading I have found that using penalized maximum likelihood could help me solve this problem. Is there other ways (maybe simpler) that could help me solve the problem?
12. ### Gamma Distribution and data fitting

I have a problem with data fitting to gamma distribution. I have rainfall occurrences (calculated using 1st order 2 states Markov Chain analysis) for more than 30 yrs. I want to fit those data into Gamma Distribution and estimate parameters (Alpha and Beta). Then I want to simulate rainfall...
13. ### MLE of multinomial distribution with missing values

Hi, I am trying to solve a problem and the results I get seem counter-intuitive. We randomly throw n balls into an area partitioned into 3 bins b_1,b_2,b_3. The size of each bins is proportional to the probability the ball will fall in it. Let's call these probabilities p_1,p_2,p_3. This...
14. ### Confirmatory factor analysis: How to deal with non-normal data

Hello, I have 12 manifest variables, none of which is normally distributed. As far as I know this makes my data unsuitable for a CFA with maximum likelihood estimation (?). I am not sure, however, which alternative estimation method should be used instead. Apart from practical advice I am...
15. ### Maximum Likelihood Estimation Exercise (short)

Hi I have found the following exercise while trying to understand the Maximum Likelihood Estimation in Practice: "In a random sample of 1000 Swiss employees, 78% stated that they received a pay increase for the current year. What is the MLE for the share of employees with a pay raise?"...
16. ### estimation parameters using maximum likelihood

Hi everyone! I‘m trying to estimate the parameters of a simple model, but I keep getting the same error message: „could not calculate numerical derivatives missing values encountered, flat or discontinuous region encountered“ program define logit_error1 *** args lnf q alpha beta mu ***...
17. ### Help with unbiased estimators and efficiency

Suppose that Y1, Y2, ..., Yn constitute a random sample from the density function f(y|t) = e^-(y-t), y>t where t is an unknown positive constant a. Find an estimator t1(hat) for t by the method of moments b. Find an estimator t2(hat) for t by the method of maximum likelihood c...
18. ### Indefinite covariance matrix

Hi all. I have a situation regarding maximum likelihood estimation. As per usual i maximize the likelihood function, but the hessian comes out with one or two small negative eigenvalues. I know that in principle this means that i found a saddle point, but it seems that my estimates are...
19. ### method of maximum likelihood

Hi, i know this is a long question but help would be greatly appreciated as ive no idea where to start, here it is: Let x1, x2, . . . , xn be an iid sample from a Gamma distribution with known shape parameter α and scale parameter β = 1/σ. . (a) Derive an estimate of σ using method of maximum...