Empirical Survivor Function (esf)

#1
From page 26, chapter 2 of the reference "Tableman, M., & Kim, J. S. (2003). Survival analysis using S: analysis of time-to-event data. CRC press", I have found the definition of the empirical survivor function (esf) is

S(t) = (number of individuals > t)/n .

But from page 80, chapter 3 of the reference "Lawless, J. F. (2011). Statistical models and methods for lifetime data (Vol. 362). John Wiley & Sons",

esf, S(t) = (number of individuals >= t)/n .

Which formula is correct?

Consider a lifetime data:

t = 9 13 13 18 33 28 31 34

By the definition of esf from the first reference, S(18)= 4/8=0.5.

By the definition of esf from the second reference, S(18)= 5/8=0.625.

Which one is conventional?

Thanks for your attention.
 

rogojel

TS Contributor
#2
hi,
consider that at S(19) both definitions have the same value . As in general the value at a given point is much less important then the general shape of the function, I would say that both definitions are ok as long as used consistently.