The normal distribution is defined from wikipedia as:
Is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
But why is it a kind of probability distribution and not a type of probability density?*
The shape of the curve of Probability density function is the shape of the probabilities that the random variable takes, for example in the normal distribution the most probable values are in the highest region of the curve.
Therefore, the PDF gives us information on the form that the possible values of the random variable will take. And the CDF gives us the probability that the random variable takes values less than or equal to a certain value $ n $, so this makes me think,
Why is it a type of distribution and not a density type? Therefore, it should be called normal density
EDIT: I think that something called "Distribution" tells me how the values are distributed. And this I can know just by looking at the graph. And it is precisely this information that I obtain with the density function. So, what error of concepts do I have?
Best Answer
The difference between a probability distribution and a probability density is that the latter is a special case of the former. In fact, the reason the normal distribution is commonly is due to the fact it happens to be the distribution one gets in the central limit theorem. In general, a probability distribution need not have a density (the precise property is that the probability distribution is absolutely continuous with respect to the Lebesgue measure). It just turns out that the distribution arising from the central limit theorem has this property, and therefore the normal density exists - with one caveat! Namely, there is such a thing as a normal distribution with variance zero. It describes the distribution of a deterministic number. Its distribution is known as the dirac delta "function", which has no true density. If it did have a density, it would spike to infinity at the deterministic number, and be zero everywhere else.