Fig. 1

Various cases of the probability density functions of the Weibull distribution generated by varying shape parameter \(\alpha\) and scale parameter \(\lambda = 1\). a \(\alpha \rightarrow \infty\) produces a nearly singular distribution at \(\lambda\). b \(\alpha =3.4\) produces a Gaussian-like distribution. c \(\alpha =2\) produces a Rayleigh distribution. d \(\alpha =1\) produces an exponential distribution. e \(\alpha < 1\) produces a heavy-tailed distribution