Page 252 - DMTH404_STATISTICS

Statistics

Notes

The log-normal distribution with parameters  and  > 0 has density function

1  (ln(t) ) 2
2
g(t)  e 2 , t  0.
2 t
Its failure rate function is given by

1  log t   
 (t)  Z   ,
t    
where Z is the standard normal hazard function, which is IFR.

The behavior of the failure rate function for the log-normal distribution depends on s :
“For s  1.0, (t) is roughly constant. For   0.4, (t) increases…. For   1.5, l(t) decreases. This
flexibility makes the lognormal distribution popular and suitable for many products.”

244 LOVELY PROFESSIONAL UNIVERSITY