Linked Questions

1 vote
1 answer

Why is the likelihood a product of pdf terms $f(\theta; x_1, x_2, ...)$ [duplicate]

Before anyone says this has been answered elsewhere I don't think it has. The likelihood is given by: $$ L(θ;x_1,\cdots, x_n) = \prod^n_i f(x_i\mid\theta)$$ where $f$ is the probability density ...
rhody's user avatar
  • 215
4 votes
0 answers

How is maximum likelihood estimation method defined for non-continuous and non-discrete distributions? [duplicate]

Consider a task of estimating a parameter of a censored exponential distribution using maximum likelihood estimation. The typical approach to this question is presented in this question. The linked ...
gregorias's user avatar
  • 161
0 votes
1 answer

Lost in the introduction discussing probability/likelihood [duplicate]

I have some questions about the following paragraph which introduces a masters level course. In this unit we consider the Frequentist (i.e. counting) approach to statistical inference and computing ...
Kirsten's user avatar
  • 713
0 votes
0 answers

Confusion about Maximum likelihood estimation [duplicate]

How can I see that the maximum likelihood approach finds the parameter values of the probability distribution that maximize the probability of the observed sample? Maximum likelihood is not the ...
Alex's user avatar
  • 93
8 votes
5 answers

Probability that the sample comes from a certain distribution

Assume we have a data sample: $x_{1}, \dots, x_{n}$ from $n$ i.i.d. continuous random variables. Then, for simplicity, let us consider two distributions, $f(x)$ and $g(x)$. Is there any statistical ...
phibog's user avatar
  • 81
6 votes
4 answers

Why does Maximum Likelihood estimation maximize probability density instead of probability

I am trying to understand Maximum likelihood estimation but it looks like I am missing something rather elementary. suppose we have an iid random sample $X_1, X_2,..., X_n$ for which the ...
Curious's user avatar
  • 61
8 votes
3 answers

Estimating $\theta$ based on censored data when $X_i\sim \text{Uniform}(0,\theta)$ with $\theta\ge 1$

Suppose $(X_i)_{1\le i\le n}$ are i.i.d $\text{Uniform}(0,\theta)$ random variables where $\theta \ge 1$. We observe $Y_i=\min(X_i,1)$ instead of $X_i$. I wish to estimate $\theta$ based on the data $(...
StubbornAtom's user avatar
  • 10.7k
1 vote
1 answer

Maximum Likelihood Estimator for Censored Data

Let $X^n=(X_1,X_2,...,X_n)$ denote a sample where (1) $X_i=\mathbf 1_{(\epsilon_i + \mu \geq 0)}(\mu+\epsilon_i)+\mathbf 1_{(\epsilon_i + \mu \leq 1)}(\mu+\epsilon_i)+\mathbf 1_{(\epsilon_i + \mu &...
user_newbie10's user avatar
6 votes
1 answer

Units for likelihoods and probabilities

In this discussion by comments Is the exact value of any likelihood meaningless?, it was suggested (firmly!) that likelihoods and probabilities calculated from continuous data not only have units, but ...
Michael Lew's user avatar
  • 13.8k
-1 votes
1 answer

MLE - CDF vs PDF as the likelihood-function?

Would maximum-likelihood estimation: with the cumulative-distribution function as the likelihood-function and the probability-density function as the likelihood-function, yield the same/equal ...
x.projekt's user avatar
  • 240
7 votes
2 answers

Measure-Theoretic Definition of MLE

This question really boils down to the following: Under what conditions can we refer to pointwise values of a probability density function? Obviously continuity of the pdf suffices, but because of the ...
Robert Bassett's user avatar
1 vote
1 answer

Truncated normal distribution without scaling

My understanding of a truncated normal distribution $\mathcal{N}(\mu,\sigma;a,b)$ is that it results from scaling the values of a normal distribution within the bounds $[a; b]$ such that the area ...
monade's user avatar
  • 509
1 vote
1 answer

Mixture distribution PDF with discrete values

I am having problems while defining the PDF expression of a mixture distribution when some of its values are discrete. For example, imagine that a given random variable $\mathbb{X}$ takes values as ...
Gabriel's user avatar
  • 75
1 vote
1 answer

Fitting discrete data to continuous distributions

I'm creating a simulation model, in which some stochastic factors are included. On of my stochastic factors is the amount of containers arriving daily for a specific delivery location. A plot of this ...
Aron T.'s user avatar
  • 113
4 votes
1 answer

Invariance of maximum likelihood estimates to rearrangements of parameters/constants in the model?

I know that maximum likelihood estimates are invariant to re-parametrization ( Is the MLE also invariant to rearrangements of the constants and ...
Mon2's user avatar
  • 43

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