Table 2.

The example linear (dF/dt) and logarithmic (dF/dτ) PDFs.

		dF/dt	dF/dτ
Power Law	t > t0	$(\alpha -1)t^{-\alpha }/t_0^{-\alpha +1}$	ln(10) (α − 1)(t/ t0)− α+1
Exponential	t > t1	λe− λ(t− t1)	ln(10) λte− λ(t− t1)
Gamma	t > 0	$\frac{t^{\xi -1}{e}^{-t/\theta }}{{\theta }^{\xi }\mathit{\Gamma }(\xi )}$	$ln(10)\frac{t^{\xi }{e}^{-t/\theta }}{{\theta }^{\xi }\mathit{\Gamma }(\xi )}$
Periodic Log- Normal	t > 0	$\frac{\rho /(\mathit{tln}(10))}{\sqrt{2\pi }\mathit{log}(\sigma )}{\displaystyle \sum _{k=1}^{\infty }}{(1-\rho )}^{k-1}{e}^{-{\left(\frac{\mathit{log}(t/\mu k)}{\sqrt{2}\mathit{log}(\sigma )}\right)}^2}$	$\frac{\rho }{\sqrt{2\pi }\mathit{log}(\sigma )}{\displaystyle \sum _{k=1}^{\infty }}{(1-\rho )}^{k-1}{e}^{-{\left(\frac{\mathit{log}(t/\mu k)}{\sqrt{2}\mathit{log}(\sigma )}\right)}^2}$