# Questions tagged [maximum-likelihood]

For questions that use the method of maximum likelihood for estimating the parameters of a statistical model with given data.

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### Proof of the unbiasedness of an estimate obtained by gradient search

As the solution to an MLE problem cannot be obtained analytically, I apply gradient search to find the solution $\hat{\theta}$ to satisfies \begin{align} \frac{\partial \mathcal{L}(\mathbf{y}\mid\...
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### Question about MLE estimator for simple exercise

As I am working through my old university notes, due to excess of time lately, I've stumbled upon the following exercise: Let's consider a medical treatment in which the same drug is used twice. We ...
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### Estimate size of population using hyper geometric distribution and maximum likelihood estimator

I saw the following in my notes, but I can’t quite remember why the argument holds... could someone help me please? Suppose there are N number of fishes in a lake and we want to estimate N. We catch ...
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### Maximum likelihood estimator - Uniform distribution [closed]

Let X have an uniform distribution on the segment [a,b]. With the method of maximum likelihood, estimate the parameter d = b-a. Then check if the estimator is consistent. Hi, i tried solving this ...
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### How to find MLE from a cumulative distribution function?

I'm new to probability. Given the cumulative distribution function $f_Y(y)=\theta e^{-y\theta}$ defined from 0 to infinity, I would like to find the parameter $\theta$ such that it maximizes the ...
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### Bias and variance of maximum likelihood estimator

An exponential distribution has a probability density function: $$p(y|v) = exp(−e^{−v}y − v)$$ It has one parameter: a log-scale parameter $v$. If a random variable follows a gamma distribution with ...
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### What is the Probability density function of MLE

Given a random sample of size N from a population with probability density function $f(x)$ that depends on a paramter $\hat{A}$. Its MLE is the minimun of the random sample. Now, I have been asked to ...