Hey Thadathon,

Location and scale are the two parameters which characterize the shape of a probability distribution. The location depicts where the distribution is located on the x-axis (where it's centered), while the scale depicts how spread-out (wide & tall) the graph is.

In statistics, every probability distribution has a moment-generating function (or MGF for short) and we can use said function to:
1.) Get the standard form of the distribution equation.
2.) Find the various moments (and central moments) of the distribution.

Thus, another way to think about these is that location and scale define the "specific" type of, say, Normal distribution we're looking at. In the case of the normal distribution, the location is equal to the population mean, while the scale is the population standard deviation. Hence, the location and scale determine the exact shape of the Normal distribution.

For the Logistic distribution, it's pretty much the same, because if a random variable Z follows the standard logistic distribution, then for any real parameter a, and any positive parameter b, the random variable X = a + bZ follows the logistic distribution (and has a location = a, and scale = b).

Hope this helps!
Best,
365 Vik

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