A Step-by-Step Guide to Generating Descending Weights that Sum to 100 in Python

Weighted averages are often used in many fields, such as finance, statistics, and data analysis. A weighted average is an average where some numbers contribute more to the final result than others. For example, suppose you want to calculate your grade in a class. The grade for each assignment contributes differently to your overall grade. You may use a weighted average to determine the final grade, with each assignment's weight being its percentage of the overall grade. In this case, the weights sum up to 100%.

However, assigning weights can be challenging, especially if the number of weights is high. In such cases, generating weights that sum up to 100% can be time-consuming and challenging. In this article, we will discuss an algorithmic approach to generate descending weights that sum to 100.

The algorithm we will use is straightforward and involves only a few calculations. We will use the NumPy library, which is a popular Python library for numerical computing. The algorithm takes one argument, ui, which represents the number of splits. The algorithm will generate descending weights starting with the highest weight and ending with the lowest. The weights will sum to 100.

The first step in the algorithm is to calculate the split ratio or the smoothing factor. We use the formula 200/(ui*(ui-1)) to calculate the split ratio. This formula is used to calculate the difference between each consecutive weight value.

d1 = 200/(ui*(ui-1))

Next, we check if the split ratio is greater than 5. If it is, we set the smoothing factor to 5.

if d1 > 5: d = 5

If the split ratio is less than or equal to 5, we subtract a small value from the split ratio to reduce the roundoff error.

else: d = d1 - 0.000001

The next step in the algorithm is to calculate the first highest number. We add (d*(ui-1))/2 to 100/ui to calculate the first highest number. This is done to ensure that the sum of all weights is equal to 100.

x0 = (100/ui) + ((d*(ui-1))/2)

We then initialize an empty list named weights to store the weight values.

weights = []

The variable new is assigned the value of x0, which is the first highest number.

new = x0

Next, we use a for loop to generate the descending weight values. The loop runs ui times, which is the number of splits. Inside the loop, we append the current value of new to the weights list, and then subtract the smoothing factor from new to get the next weight value.

for i in range(ui): weights.append(new) new -= d

Finally, we return the weight values as a NumPy array of float32 data type.

return np.array(weights, dtype=np.float32)

You can find the python code for this function at the following Github repository: https://github.com/rakeshwar07/Python_

Descending Weights Vs Exponential Smoothing:

Descending weights and exponential smoothing are two methods used to smooth time series data. Although they might look alike, they are different in their approach and application. Exponential smoothing is a statistical method used to model time series data by giving more weight to recent observations and less weight to older observations. On the other hand, descending weights assign equal weights to a fixed number of most recent observations, with the weights decreasing in a descending fashion. This approach is often used in statistical process control, where the most recent observations are given more importance.

Uses and Applications of Descending Weights that Sum up to 100: Descending weights that sum up to 100 are widely used in statistical applications such as survey sampling, market research, and decision-making processes. In survey sampling, these weights are used to adjust for differences in selection probabilities and nonresponse. In market research, these weights are used to adjust for the differences in the number of observations in different categories. In decision-making processes, these weights are used to give more importance to recent observations and to adjust for the differences in the magnitude of different variables.

Applications of Descending Weights that Sum up to 100:

1. Survey Sampling: A survey might assign higher weights to respondents who are more representative of the population being studied.

2. Market Research: A company might assign higher weights to a particular market segment that represents a large potential customer base.

3. Decision-Making Processes: A company might assign higher weights to a particular strategic option that is expected to have a greater impact on the business.

In summary, this algorithm provides a straightforward and easy-to-use approach for generating descending weights that sum up to 100%. This algorithm is particularly useful for data scientists, statisticians, and other professionals who need to work with weighted averages. The algorithm is efficient and produces accurate results. It can be easily integrated into various applications and programming languages. Although it looks similar to exponential smoothing this is different from it. In the future, I will share one of my use cases in stock market pattern recognition. I hope this article has provided you with a valuable tool that you can use in your work.