1 vote
825 views

### 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 ...
649 views

### 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 ...
72 views

### 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 ...
19 views

### 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 ...
6k views

### 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 ...
4k views

### 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 ...
466 views

652 views

### 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 ...
1k views

### 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 ...
825 views

### 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 ...
1 vote
644 views

### 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 ...
1 vote
737 views

### 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 ...
1 vote
276 views

### 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 ...