I read an article on Logistic Regression on Wikipedia: .
It was written that logistic function is a cumulative logistic distribution.
My question is what is "cumulative logistic distribution"?
$\endgroup$1 Answer
$\begingroup$The logistic distribution is a probability distribution (also called a probability density function or PDF) whose cumulative distribution function (CDF) is a logistic function.
Let's say your (continuous) $PDF(x)$ takes some variable $x$. To get the probability that $x$ lies in some interval $(a,b)$, you calculate the integral $$\int_a^b PDF(x)dx.$$
Let's denote the CDF associated with $PDF(x)$ by $CDF(x)$. $CDF(x)$ will then give the probability that the random variable $X$ that your PDF described takes a value less than or equal to $x$. So
$$CDF(x)=\int_{-\infty}^x PDF(x) dx.$$
So that was how a CDF is defined. For the logistic distribution, the CDF happens to be a logistic function (with some choice of parameters that ensure the right properties).
I know this was a lot of links. Try looking at some of the pictures in the Wikipedia articles. For instance, take a look at the PDF for the Normal distribution:
The different colors simply represent different choices of parameters. Let's focus on the red one in the middle.
Now let's look at the corresponding CDF:
The red curve here is created by going left to right along the red curve in the PDF picture above, all the while adding (accumulating) the values of the PDF along the way. So the value of the CDF at some point is equal to the area under the curve of the red PDF from $-\infty$ to $x$ (which is just another way of stating the integral).
I hope that helps.
$\endgroup$ 1
