Forecasting of solar activity is extremely important, due to its impact on our space-based technology. In recent years, we have observed a continuous decline in the peak sunspot number for Solar Cycles (SCs) 21 to 24. We are more curious about peak activity of SC 25 because if the solar activity weakens further, then it may be an indication of new extended minima. So far, the daily sunspot-number data make up the longest observational series of the solar activity available, and recently this has been replaced with the corrected new Version 2.0 sunspot-number series. In general, different prediction models are available to forecast the peak smoothed sunspot number (SSN) of the upcoming SC but they are based on the older Version 1.0 sunspot data. Therefore, it is necessary to check the applicability of earlier proposed models to predict the peak SSN using the Version 2.0 sunspot-number series. Here, we re-evaluate one such earlier proposed prediction model, which is based on the estimates of the Shannon entropy, a measure of randomness, for Version 2.0 sunspot data. We find that this prediction model is applicable to the Version 2.0 sunspot-number series. To verify the robustness of the prediction model, we used the histogram and additionally the kernel density estimator (KDE) method to calculate the probability distribution function (PDF). The estimate of the PDF is a prerequisite to compute the Shannon entropy. We found that the prediction model is robust and the correlation coefficients between model parameters are 0.93 and 0.92, respectively, for these two approaches. This exercise provides a new prediction model for the peak SSN based on the Version 2.0 sunspot-number series. The model forecasts the peak smoothed sunspot number of 136.9 ± 24 $136.9\pm 24$ using a histogram-derived PDF and 150.7 ± 25 $150.7\pm 25$ using a KDE-derived PDF for the upcoming SC 25. These predictions for SC 25 are more reliable as up to date (December 2020) sunspot-number data have been utilized to get the entropy in the end phase of SC 24. It suggests that SC 25 would be similar or slightly stronger than SC 24.

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太阳黑子数量的随机性：预测太阳周期的线索 25

太阳活动的预测极其重要，因为它对我们的太空技术有影响。近年来，我们观察到太阳活动周期 (SCs) 21 到 24 的峰值太阳黑子数量持续下降。我们对 SC 25 的峰值活动更加好奇，因为如果太阳活动进一步减弱，那么它可能表明新的扩展最小值。到目前为止，每日太阳黑子数数据构成了可用的最长太阳活动观测序列，最近这已被更正的新版本 2.0 太阳黑子数序列所取代。通常，不同的预测模型可用于预测即将到来的 SC 的峰值平滑太阳黑子数 (SSN)，但它们基于较旧的 1.0 版太阳黑子数据。所以，有必要检查早期提出的模型的适用性，以使用 2.0 版太阳黑子数系列预测峰值 SSN。在这里，我们重新评估了一个早期提出的预测模型，该模型基于香农熵（一种随机性度量）的估计，用于 2.0 版太阳黑子数据。我们发现该预测模型适用于2.0版本的太阳黑子数序列。为了验证预测模型的稳健性，我们使用直方图和额外的核密度估计器 (KDE) 方法来计算概率分布函数 (PDF)。PDF 的估计是计算香农熵的先决条件。我们发现预测模型是稳健的，这两种方法的模型参数之间的相关系数分别为 0.93 和 0.92。本练习为基于 2.0 版太阳黑子数系列的峰值 SSN 提供了一个新的预测模型。该模型使用直方图导出的 PDF 预测峰值平滑太阳黑子数为 136.9 ± 24 $136.9\pm 24$，使用 KDE 导出的 PDF 预测 150.7 ± 25 $150.7\pm 25$ 用于即将到来的 SC 25。这些对 SC 25 的预测更可靠，因为最新（2020 年 12 月）太阳黑子数数据已被用于获得 SC 24 末期的熵。这表明 SC 25 将与 SC 24 相似或略强。