Computing the ECDF

In this exercise, you will write a function that takes as input a 1D array of data and then returns the x and y values of the ECDF. You will use this function over and over again throughout this course and its sequel. ECDFs are among the most important plots in statistical analysis. You can write your own function, foo(x,y) according to the following skeleton:

def foo(a,b):
    """State what function does here"""
    # Computation performed here
    return x, y

The function foo() above takes two arguments a and b and returns two values x and y. The function header def foo(a,b): contains the function signature foo(a,b), which consists of the function name, along with its parameters.

This exercise is part of the course

Statistical Thinking in Python (Part 1)

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Exercise instructions

Define a function with the signature ecdf(data). Within the function definition,
- Compute the number of data points, n, using the len() function.
- The \(x\)-values are the sorted data. Use the np.sort() function to perform the sorting.
- The \(y\) data of the ECDF go from 1/n to 1 in equally spaced increments. You can construct this using np.arange(). Remember, however, that the end value in np.arange() is not inclusive. Therefore, np.arange() will need to go from 1 to n+1. Be sure to divide this by n.
- The function returns the values x and y.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

def ecdf(data):
    """Compute ECDF for a one-dimensional array of measurements."""
    # Number of data points: n
    ____ = ____(____)

    # x-data for the ECDF: x
    ____ = ____(____)

    # y-data for the ECDF: y
    ____ = ____(____, ____) / n

    return x, y

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