Question

I'm being asked to compute the probablity density at (0,0) using the above KDE function. i finished the previous related part. Not entirely sure of the syntax needed to enter the equation using NumPy.

Code for previous related part for reference:

Exercise 3 Based on the KDE function: Compute the probablity density at [e,e], i.e., f((0, 0)). This should return a scalar value. (2 points) : def compute (data, h): ##CODE HERE## return x i We turn our attention to another question, what is the probability distribution of data? A powerful method is kernel density estimation (KDE). The probability density function is given by where K(z) = exp(-1 r) is a kernel function and 2 i the squared euclidean norm). Hint: You can use z numpy.linal g. norm Exercise 2 Implement K(Z) based on the above kernel function. Return a numpy array with shape (500,) (2 points) def kernel(z): # z: (N, 2) numpy . array # returns (N. 1) numpy.array kzeet[] for i in range (e,len(z)): dat-z[i] norm-np.linalg.norm(dat, ord-2) kzee.append ( (1/(np.sqrt (2"math.pi)))*np.exp ( -(norm* *2/2))) return np.array(k_zee)

Answer 1

Please let me know if you require any further assistance.

The symbol Σ (f(x)) over a range simply means that you need to sum f(x) for a certain range (1 to N in this case). Therefore Σ doesn't require any special function and thus can be done using a simple 'for' loop. Although it can be made more complicated by doing it using lambda functions etc.

Here is how you will code it simply without any specialized functions.

In your case suppose you want to store the result of the above summation in a variable 'Sum' then -:

                    Sum=0

                    for i in range(1,N+1):                                                       # n+1 since range(x,y) y is not inclusive

                        Sum= Sum+(1/N)(K)((x-xi)/h)                                       # Remember to put accurate values of the various       # variables(K , x , xi and h) by calling their respective functions/values