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Bitwise
Bitwise
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You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.

The number of Y values will determine the "resolution" of the curve, so if you assume a straight line between every two adjacent Y points you can calculate an approximation of the area under the curve between those two points.

To determine the probability of an $x$ value $P(x_a<x<x_b)$:

$P(x_a<x<x_b)=y_a+..+y_b$

The result will be more accurate the more $y$ values you have.

You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.

The number of Y values will determine the "resolution" of the curve, so if you assume a straight line between every two adjacent Y points you can calculate an approximation of the area under the curve between those two points.

You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.

The number of Y values will determine the "resolution" of the curve, so if you assume a straight line between every two adjacent Y points you can calculate an approximation of the area under the curve between those two points.

To determine the probability of an $x$ value $P(x_a<x<x_b)$:

$P(x_a<x<x_b)=y_a+..+y_b$

The result will be more accurate the more $y$ values you have.

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Bitwise
Bitwise
  • 6.7k
  • 2
  • 27
  • 30

You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.

The number of Y values will determine the "resolution" of the curve, so if you assume a straight line between every two adjacent Y points you can calculate an approximation of the area under the curve between those two points.

You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.

You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.

The number of Y values will determine the "resolution" of the curve, so if you assume a straight line between every two adjacent Y points you can calculate an approximation of the area under the curve between those two points.

Source Link
Bitwise
Bitwise
  • 6.7k
  • 2
  • 27
  • 30

You can think of the Kernel Density Estimation as a smoothed histogram. Histograms are limited by the fact that they are inherently discrete (via bins) and are thus more appropriate for displaying data on discrete variables and can be very sensitive to bin size.

What you are actually doing with the Kernel Density Estimation is estimating the probability density function. This makes the interpretation straightforward. So the area under the curve is 1, and the probability of a value being between x1 and x2 is the area under the curve between those two points.