what is the excel equation for solving for the cdf in gaussian kernel estimation?

what is the excel equation for solving for the cdf in gaussian kernel estimation?

• A. = norm.dist(x, x_i, bandwidth, FALSE)
• B. = norm.dist(x, x_i, bandwidth, TRUE)
• C. = norm.dist(x_i, x, bandwidth, TRUE)
• D. = norm.dist(x, x_i, bandwidth^2, TRUE)

Answer: (B)

The key idea is that the CDF contribution of a Gaussian kernel centered at x_i with bandwidth h is the standard normal CDF evaluated at (x − x_i)/h, which is Φ((x − x_i)/h). In Excel this is obtained by the normal CDF function with those parameters: NORM.DIST(x, x_i, h, TRUE). That yields the probability P(X ≤ x) for X ~ N(x_i, h^2), which matches the kernel’s CDF form. Using the CDF flag is essential; using FALSE would give the density instead of the CDF. Swapping the order or using bandwidth^2 would mis-specify the distribution. So the correct form is NORM.DIST(x, x_i, bandwidth, TRUE).

The key idea is that the CDF contribution of a Gaussian kernel centered at x_i with bandwidth h is the standard normal CDF evaluated at (x − x_i)/h, which is Φ((x − x_i)/h). In Excel this is obtained by the normal CDF function with those parameters: NORM.DIST(x, x_i, h, TRUE). That yields the probability P(X ≤ x) for X ~ N(x_i, h^2), which matches the kernel’s CDF form.

Using the CDF flag is essential; using FALSE would give the density instead of the CDF. Swapping the order or using bandwidth^2 would mis-specify the distribution. So the correct form is NORM.DIST(x, x_i, bandwidth, TRUE).