Question

Density function is to be estimated using a normal kernel with a variance of 2. Data points are located at x = 1,3,4. What is the equation of the estimated density function

Answer 1

Suppose we have some variable X ∼ f(x) where f(x) is the probability

density function (pdf) of X.

Note that we have two requirements on f(x):

f(x) ≥ 0 for all x ∈ X , where X is the domain of X

R

X

f(x)dx = 1

Example: normal distribution pdf has the form

f(x) = 1

σ

√

2π

e

−

(x−µ)

2

2σ2

which is well-defined for all x, µ ∈ R and σ ∈ R

+.

Nathaniel E. Helwig (U of Minnesota) Density and Distribution Estimation U