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  1. A solar cycle (SC) is typically characterized by a plot of sunspot number as a function of time. This plot usually has a sharp rising phase, followed by leveling inflection towards the peak (or peaks) of solar maximum, followed by a downward inflection and a trailing declining phase. The overall shape is not symmetric and is most often characterized by a positiveness skewness. The exact shape of each SC plot varies, some tall and narrow, others short and wide, faster or slower rise times, higher or lower maxima, longer or shorter declining phases, etc. Several probability density functions (PDFs) provide adjustable parameters that can provide a good curve fit and model the characteristics of the SC plot described above. (Note that in this exercise there is no probability that's being a modeled - it is simply that the formula that describes the PDF happens to provide a good curve fit to observed data with appropriate parameter values.) The Weibull probability density function is relatively simple, typically defined by 2 parameters: shape and scale. https://statisticsbyjim.com/probability/weibull-distribution/ With some iteration, it is possible to converge on values for these 2 parameters for a Weibull distribution that provide a pretty good match to historical SC plots, shown here for SC20-SC24: https://ibb.co/7jdhb1f
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