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Probability density function of the sample maximum of a random variable. 1. Difference between joint ...
For a probability density function, there's a big hint in the name: it's a density. You're right, though, that we don't often think of this Y-axis as all that important. PDFs are plotted all the time without any labeled Y-axis. But if you were to label it, you would read it as a density: the sum probability of some unit range in X.
This example shows the probability density function for a Gamma distribution (with shape parameter of $3/2$ and scale of $1/5$). Because most of the density is less than $1$, the curve has to rise higher than $1$ in order to have a total area of $1$ as required for all probability distributions.
4. Density estimator. Some modern computer programs have the ability to piece together curves of various shapes in such a way as to approximate the density function of the population from which a sample was chosen. (The result is sometimes called a 'spline'.) One method is called 'kernel density estimation'.
During my research, I have repeatedly come across the terms probability measure and probability density function (pdf). I am familiar with the concept of a pdf, but I am not entirely sure how probability measures relate to pdfs, or where exactly the differences lie in theoretical terms.
A probability density function (pdf) is a non-negative function that integrates to $1$. The likelihood is defined as the joint density of the observed data as a function of the parameter. But, as pointed out by the reference to Lehmann made by @whuber in a comment below, the likelihood function is a function of the parameter only, with the data ...
Could you please explain to me why the probability density function of a sine wave looks like it does, i.e. like a basket with the greatest probability density located at -1 and 1 points, decreasing towards the centre? Since each value appears twice over one period of the sine wave, wouldn't the probability of each value be the same?
It might help you to realise that the vertical axis is measured as a probability density. So if the horizontal axis is measured in km, then the vertical axis is measured as a probability density "per km". Suppose we draw a rectangular element on such a grid, which is 5 "km" wide and 0.1 "per km" high (which you might prefer to write as "km$^{-1
The wikipedia page claims that likelihood and probability are distinct concepts.. In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a clear distinction in perspective: the number that is the probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the ...
Intuition for how the cumulative probability distribution can be derived from probability density function? 1 Deriving the joint probability density function from a given marginal density function and conditional density function