C#: Split a Single Annual Figure into Monthly amounts based on an arbitrary Y=f(X) formula

Question

I have an annual figure, let's say for purposes of this question that the figure is 100%.

What I would like to do is have C# split the 100% figure into a curved distribution of monthly percentages based on a specific formula Y = f(X), that still add to 100.

This is likely primarily a math question - how could I accomplish this without manually keying in figures that add to 100?

Answer 1

My comment as an answer. The way to do this is to get the seasonality curve expressed over time. Let's consider a simple case, where we the curve looks like a step-ish sine-ish curve. We'll use a unit of "percentage of maximum value" to describe the curve. Seasons will be 3 months long, so winter is Dec-Feb, spring is Mar-May, etc.

The curve looks like:

Dec-Feb	Mar-May	Jun-Aug	Sep-Nov
20% of Max	60% of Max	100% of Max	60% of Max

If you add those all up (for 12 months), you will get 720%, or 7.2. So, the actual values you want to use are:

Dec-Feb	Mar-May	Jun-Aug	Sep-Nov
2.78 (i.e., 20.0/7.2)	8.33 (60.0/7.2)	13.89 (100.0/7.2)	8.33 (60.0/7.2)

Checking this to make sure it's valid:

2.78 * 3 + 8.33 * 6 + 13.89 *3 = 99.99 (or, just about 100)

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Some working sample code for a C# console app using an arbitrary sinusoidal function that vaguely represents some early and late seasonality - MyFunction can be replaced with any function, including a stepwise one like above:

using System;
using System.Linq;
namespace Test
{
class Program
{
    static void Main(string[] args)
    {

        int months = 12;

        double[] scaleExpectations = new double[months];

        for (int i = 0; i < 12; i++)
        {
            scaleExpectations[i] = MyFunction(i);
        }

        double sum = scaleExpectations.Sum(); //this is the actual Integral of the series, since it is not a real curve

        double[] percents = new double[months];

        for (int i = 0; i < 12; i++)
        {
            percents[i] = Math.Round((scaleExpectations[i] * 100) / sum, 2);

            Console.WriteLine($"iteration {i} with value {percents[i]}");

            if (i == 11) // remove rounding error by altering last position
            {
                var error = 100 - percents.Sum();
                percents[i] = percents[i] + error;
            }
        }

        Console.WriteLine(percents.Sum());

    }

    public static double MyFunction(double input)
    {
        return .4 * Math.Sin(.5 * (input - 7.5)) + .9;
    }
}
}