would like to have added to an additional life distribution to show up along with standard list of Weibull, Exponential, Lognormal, DS Weibull, etc
the Cumulative Distribution Function for this life distribution is given by
F(t|p,a,y) = 1 - exp(p*exp(-t/a) - y t -p)
or expressed equivalently
F(t|a,y,x) = 1 - exp(ax*exp(-t/a) - y t - a x)
and corresponds to a hazard function starting at failure rate (y+x) which decays exponentially with time constant a to constant failure rate y .... here, the equivalent Defective Sub-population proportion p=ax in the limit that y is zero
have found that for some datasets, the BIC figure of merit for this life distribution is lower than that of other early/mid bathtub curve options
would like to have life distribution platform compute the standard set of estimates, covariance matrix etc for this three-parameter life distribution