maybe take a look at the Gamma family of distributions, specifically the Weibull distribution.
also, in the life distribution platform you can fit a mixture of distributions,

This data set using 10000 rows with this formula:
Abs( Random Normal( 1, 1 ) )
Analyze>Reliability>Life Distribution, I picked the formula col for the time to event and from the red triangle picked fit mixture. This shows up at the bottom of the report, I click Weibull twice, and then clicked Go

Life Distribution(
Y( :Column 3 ),
Confidence Interval Method( Wald ),
Interval Type( Pointwise ),
Show Event Plot Frequency Label( 0 ),
Fit Mixture( Mix( Weibull( 2 ), Overlapping Clusters, Show Profilers( 0 ) ) ),
SendToReport(
Dispatch( {"Mixture", "Overlay"}, "5", ScaleBox,
{Format( "Fixed Dec", 12, 1 ), Min( -0.0507969202844342 ),
Max( 1.05079692028443 ), Inc( 0.2 ), Minor Ticks( 0 )}
),
Dispatch( {"Mixture", "Overlay"}, "4", ScaleBox,
{Format( "Fixed Dec", 12, 0 ), Min( -0.401614772053014 ),
Max( 5.23133596019622 ), Inc( 1 ), Minor Ticks( 0 )}
)
)
);
JMP Systems Engineer, Health and Life Sciences (Pharma)