Editing Weibull distribution (section)

====First alternative====
Applications in [[medical statistics]] and [[econometrics]] often adopt a different parameterization.<ref>{{cite book |last=Collett |first=David |title=Modelling survival data in medical research |location=Boca Raton |publisher=Chapman and Hall / CRC |edition=3rd |year=2015 |isbn=978-1439856789 }}</ref><ref>{{cite book |last1=Cameron |first1=A. C. |last2=Trivedi |first2=P. K. |title=Microeconometrics : methods and applications |date=2005 |isbn=978-0-521-84805-3 |page=584|publisher=Cambridge University Press }}</ref> The shape parameter ''k'' is the same as above, while the scale parameter is <math>b = \lambda^{-k}</math>. In this case, for ''x'' ≥ 0, the probability density function is
:<math>f(x;k,b) = bkx^{k-1}e^{-bx^k},</math>
the cumulative distribution function is 
:<math>F(x;k,b) = 1 - e^{-bx^k},</math>
the quantile function is 
:<math>Q(p;k,b) = \left(-\frac{1}{b}\ln(1-p) \right)^{\frac{1}{k}},</math>
the hazard function is
:<math>h(x;k,b) = bkx^{k-1},</math>

and the mean is 
:<math>b^{-1/k}\Gamma(1+1/k).</math>