0

I had a bit of a question about fitting probability density functions (specifically the Weibull Distribution) to a set of data.

I have seen a number of examples where the distribution is directly overlaid on the histogram and they both share the same axis titles and I don't fully understand why this is, specifically with the y-axis.

From my understanding, the y-value for the distribution is the probability density, which can be described as the rate that the probability is changing over the unit that x is (or the probability per x). The y-axis for the histogram is simply the number of times that a specific outcome has occurred, so I am not entirely sure how these two can be equated. Should the axis titles be different? I'm not entirely sure why the standard layout seems to be sharing the same axis title?

Here is a specific example that I have come across

user863345
  • 1
  • The histogram is (when normalized) a statistical approximation to the density function. – herb steinberg Dec 16 '20 at 22:24
  • If you do not normalize the histogram, is it still valid to fit the density function over the histogram if you adjust the scale of the distribution? Also would the y-axis of "Number" (for instance) be sufficient for the title or would that not be accurate in terms of the probability density? – user863345 Dec 18 '20 at 20:26
  • Normalization is necessary because the integral of the density function must =1. Scaling the histogram is OK to get this result. – herb steinberg Dec 18 '20 at 22:25
  • I updated the question to include the specific example I was referring to, I'm not sure if they normalized the histogram and if they haven't would that mean the graph, along with the y-axis, would be incorrect? – user863345 Jan 05 '21 at 14:52

0 Answers0