Is there any polynomial approximation to the sigmoid function $ 1/(1 + e^{-x}) $?
The sigmoid curve also known as s-curve is used to shows the sales statistics. It is ideally expected that the sales curve follows the s-curve over a fiscal year, but that doesn't always hold true in the real world. The month-wise data when plotted, somewhat resembles a sigmoid curve. But the same when plotted for week-wise data, lot of fluctuations come up, and the resulting plot doesn't look like that for a sigmoid curve. To show how it should look ideally, $y1$ is the month-wise data, and I need to fit week-wise datapoints to the sigmoid curve. It should also hold true that the sum of the sales for the four weeks in a month should be equal to the month-wise data. So given the month-wise sale, I am trying to predict the sales of each week such that the sum of the sales of the four weeks in a month is equal to the sales of that month.