Fig. 3 PDF of (a) GF, (b) Eq. (7) GMF, and (c) PDF of BF
Equation (1) is a monotonic decreasing curve when \(n-1<0\), that is, \(n<1\), which can be used to fit the IR of HS. In Eq. (3), affects the height of the curve,\(\ t_{b}\) is the temporal inflection point, which affects the distribution of the crest on the timeline, and \(\delta\) affects the width of the crest. The GF of Eq. (3) can be used to fit the IR of W-RS when the stable IR after the inflection point is equal to that before the inflection point. In Eq. (5), \(n\ \)is the order number affecting the number of crests; \(a_{i}\) and \(b_{i}\) jointly determine the height of the curve; and \(\omega\) is the angular frequency affecting the width of the crest. The FSF can be used to fit the IR of W-RS when the IR has multiple crests. BF is a monotonic decreasing curve when \(0<s\leq 1\), and can be used to fit the IR of HS. Its PDF is a single-peak curve when\(\text{\ s}>1\), and can be used to fit the IR of W-RS. The PDF of BF is a U-shaped curve when\(0<p<1\) and \(0<q<1\); when \(0<p\leq 1\) and \(q>1\), the PDF is a monotonic decreasing curve that can be used to fit the IR of HS; when \(p>1\) and \(0<q\leq 1\), the PDF is a monotonic increasing curve, and when \(p>q>1\), the PDF is a left-skew distribution curve; when \(q>p>1\), the PDF is a right-skew distribution curve that can be used to fit the IR of W-RS.