Well, we’ve got the solution for ya monotonic splines!

Now, before you start rolling your eyes and muttering “what is this guy talking about,” let me explain. Monotonic splines are a non-parametric approach to analyzing recurrent events data that don’t require any fancy assumptions or complicated math. They’re basically like connect-the-dots for nerds, but with more numbers and less fun.

So how do they work? Well, let’s say you have some software system that keeps crashing over time (because it’s a piece of junk). You want to figure out if there are any patterns or trends in the frequency of these crashes. Instead of trying to fit your data into some fancy statistical model with all sorts of assumptions and parameters, you can just draw a line between the points on a graph that connects them monotonically (i.e., it goes up or stays flat).

Here’s an example: let’s say we have this lovely dataset of software crashes over time:

| Time | Crashes |
| — | — |
| 0 | 10 |
| 5 | 20 |
| 10 | 30 |
| 15 | 40 |
| 20 | 60 |

To create a monotonic spline, we can connect the points on this graph using a series of straight lines that don’t go below any previous point. Here’s what it might look like:

# The following code creates a monotonic spline by connecting points on a graph using straight lines that do not go below any previous point.

# First, we define the x and y values for the points on the graph.
x_values = [0, 5, 10, 15, 20] # List of x values
y_values = [10, 20, 30, 40, 60] # List of y values


corrected_y_values = []

# Then, we loop through the y values and compare them to the previous value.
for i in range(len(y_values)):
    if i == 0: # For the first value, we simply add it to the corrected list.
        corrected_y_values.append(y_values[i])
    else: # For subsequent values, we check if it is lower than the previous value.
        if y_values[i] < corrected_y_values[i-1]: # If it is lower, we replace it with the previous value.
            corrected_y_values.append(corrected_y_values[i-1])
        else: # If it is not lower, we add it to the corrected list.
            corrected_y_values.append(y_values[i])


_______
/       \
/         \
/           \
/             \
\_____________/
    ^        ^
    10       20

As you can see, the line goes up monotonically from left to right. This tells us that there’s a clear trend in the frequency of software crashes over time they’re increasing at an accelerating rate!

Now, some people might argue that this is too simplistic and doesn’t take into account all sorts of other factors like system load or user behavior. And you know what? They’re right! But sometimes simplicity is better than complexity when it comes to analyzing data. Plus, monotonic splines can be a great starting point for more advanced statistical models that do take these factors into account.