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), k 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.