Algorithm 3. Event history analysis.

Input: A sequence of input data latency L= l1, l2 … ln.

Distribution model M = {Gamma, LogNormal, Weibull}.

Output: Probability density function for distribution model, Hazard rate.

• H(⋅|x) is a hazard rate that models the probability of an event to occur at time t.

• F(t) is the Probability Density Function for input data.

• μ = Scale, σ = Shape.

Step-1: Identify the suitable distribution model m ∈ M. // find the suitable distribution model

Step-2: Calculate the probability distribution function for model m. // Fit the model

$F\left(x\right)={\displaystyle \frac{{\mathrm{e}}^{-({(\ln (x/m))}^2/(2{\sigma }^2))}}{x\sigma \sqrt{2\pi }}}$

Step-3: Calculate hazard rate $H(\mathrm{x},\sigma )={\displaystyle \frac{\left({\displaystyle \frac{1}{x\sigma }}\right)\varphi \left({\displaystyle \frac{\ln x}{\sigma }}\right)}{\mathrm{\Phi }\left({\displaystyle \frac{\ln x}{\sigma }}\right)}}$ // Forecast the probability of delay