# Tag Info

### Seemingly contradiction: probability density function and maximum likelihood calculations for continuous random variable

There isn't any contradiction here. Your confusion is a very common one when dealing with the likelihood function for a continuous random variable. Let's take a step back and start from a discrete ...
• 6,428
Accepted

### Observed Fisher information for the binomial: How is $I(\hat{\theta}) = \frac{n}{\hat{\theta}(1 - \hat{\theta})}$ calculated?

Hint: Substitute the value $\hat\theta=x/n$ in $I(\theta) .$ See what happens. Substitute in place of $\theta$ to get $$\frac{n^2x}{x^2}+ \frac{n^2(n-x) }{(n-x) ^2}.$$ Simplify it.
• 3,694

• 3,694
Accepted

### Use of weights in choosing power parameter in Tweedie distribution

"How come that the weights don't play any rule in the function? Shouldn't it be taken into account when computing $\phi_{mle}$?". "... the function optimizes over the function ...
• 36

### Use of Relative Likelihoods in Statistics?

In some literature the term "plausible" for parameters is used synonymously with "high likelihood". The idea is in principle the same as the idea behind statistical tests: ...

### Use of Relative Likelihoods in Statistics?

This is an extended comment, to complement the great answers by @ChristianHennig, @SextusEmpiricus and @statmerkur, with background material from related Cross Validated threads. The theory of ...
• 7,210
Rather than a schematic graph of the score function $\dot{l}_x(\theta)$ vs $\theta$, I plot $\dot{l}_x(\theta)$ for an assortment of distributions. Then a schematic can be generalized from those cases....