# mle

1. ### Normal Distribution: MLE, UMVUE & MSE

Attached is a problem regarding MLE and UMVUE of a normal sample. Does anyone know how to do b) the MSE part? The use of An is confusing.
2. ### Fitting a distribution to data using MLE

I have a dataset to which I'd like to fit a distribution using MLE. In the old days, I would have taken a guess and then used a KS test to see if the fit were good. I've been led to believe that modern (i.e. written in the last 10 years) can do this for me. It's been a while since I've...
3. ### Dis./Avantadges of estimating of binary response model with OLS

In the Maximum Likelihood Estimator context, I can't find answers for those two questions: - What are the advantages and disadvantages of estimating of a binary response model with OLS ? - Same questions but compared to MLE ? I thank you in advance :o
4. ### Unique Solution.

Is the following statement true that : "To get unique solution of each parameter in a model, number of equations must be greater than or equal to the number of parameters." ??? Regards.
5. ### **Only for Poisson, Censored data, fitdistrplus*** the function mle failed to estimat

Hello All, I am getting the following error and it only happens for interval censoring, It does not happen for left and right censoring, and it also does not happen for exp, norm, lnorm, weibull,... I have to say I do not have any idea, > max(z) [1] 39011 > min(z) [1] 1 > I am...
6. ### Using MLE to find the right distribution

Hi, I know that MLE can be used to find the best fitting parameter assuming a that the distribution is known, but is there a way (using Excel or SAS) to find what distribution best fits the data (together with the best parameter of the distribution), in other words, the distribution is not...
7. ### Maximum Likelihood Estimator(MLE) for P

Q: Suppose we have a coin for which the probability that it lands on heads is p where p equals either 0.4 or 0.7, but we do not know which of these two values is correct. We flip the coin 3 times, letting X denote the number of times that the coin lands on heads. The probability distribution for...
8. ### How is this a MLE?

In all the literature I can find it is stated (and "proven" trivially) that for i.i.d. samples r with Rayleigh distribution \sigma the MLE is \widehat{\sigma} = \frac{\sum r_i^2}{2n}, and it is an unbiased estimator for \sigma. But any Monte Carlo test shows that's not true: Only the square...
9. ### Rayleigh estimator and correction factor

We're using the Rayleigh distribution for some real-world scenarios. We often need to estimate its parameter (sigma) from samples R of size N where N is very small. The estimator we're using for sigma, \widehat{\sigma} = \sqrt{\frac{\sum r_i^2}{2n}}, is biased. Using Monte Carlo analysis...
10. ### MLE of a weirdly split lambda in a Poisson distribution

Hi everyone! :) I'm new here. I have been looking everywhere for the solution to this problem so here's to hoping some of you can help me. :) The number of cases X of a rare disease is assumed to follow a Poisson distribution, X ~ Poi(lambda) We want to analyse the prevalence of the...
11. ### Can you give me some references?

I need the derivation of the parameters of distributions including: Gumbel, Weibal, Lognormal and Gamma with both method of moments and maximum likelihood methods. Can you introduce me some references for the full derivation? If you are referencing book I appreciate if you can do more than one...
12. ### parameter estimation by MLE method

Hi All I need to estimate two unknown parameters (lambda1 and lambda2) by using MLE. I know that they have normal distribution. h = g(lambda1 , lambda2) where h is random variable. how can I do it? I thought I should write: f(h) = Jacobian * Nor(mu1 , sigma1)*Nor(mu2 , sigma2) Also I thought...
13. ### the MLE question. what is the MLE if the variance is heteroskedasticity

The normal distribution of MLE is start {x1,,,,,xn} random sample from N(u,σ^2) This family of distributions has two parameters: θ = (μ, σ), so we maximize the likelihood, , over both parameters simultaneously using logarithm... I know this. but what if the normal distribution's {x1,,,,,xn}...
14. ### Log-likelihood MLE Markov chain

Hey! I am currently working with Markov chains and calculated the Maximum Likelihood Estimate using transition probabilities as suggested by several sources. I now want to calculate the log-likelihood of the MLE, but I am quite unsure how to do so. Maybe someone can help me out. Thanks...

16. ### Maximum Likelihood Estimate For A Poisson Mass Function ...

with mean μ is ((μ ^ x) * ((exp) ^ -μ)) / x! The log likelihood is x * log(μ) − μ. (Answer) How do I arrive at the log likelihood provided? I have tried differentiating (μ ^ x) * ((exp) ^ -μ) with respect to μ using the product rule and cannot get to the answer provided. Can...
17. ### MLE of P(X<2) - Exponential distribution

The problem statement: Find the MLE of θ = P (X≤ 2) in a random sample of size n selected from an exponential distribution EXP(λ) Relevant 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...
18. ### unrestricted cumulative probit model with vglm()---extend to a multivariate setting?

Hello. I'm trying to fit a multivariate, unrestricted cumulative probit model. I've had success in fitting a proportional odds probit model using polr(method="probit") in the MASS package and the unrestricted cumulative probit model using vglm(cumulative(link="probit)) in the VGAM package...
19. ### unrestricted cumulative probit model with vglm()---extend to a multivariate setting?

Hi, all. I'm trying to model the transition of multiple, ordinal response variables on a continuous predictor (age). In this specific case, I'm investigating the ages at which a skeletal trait passes through a series of morphological stages. In anthropological parlance, this has become known...
20. ### Very long post - need help thanks

Dear All, I am writing to you because I have got a lot of troubles with some concepts regarding Generalised Linear Models. I need to understand it by the January 2012. I hope it is possible. I am currently getting through one of the books regarding generalised linear models in a pretty much...