TEST FOR EXPONENTIAL within Weibulls - YOURNAME 1 The data as SAS sees it 12:42 Thursday, October 13, 2005 Obs days status 1 6 0 2 11 0 3 17 0 4 42 0 5 43 0 6 52 0 7 75 0 8 82 0 9 144 0 10 148 0 11 168 0 12 207 0 13 212 0 14 279 0 15 388 1 16 416 0 17 443 0 18 552 0 19 600 0 20 600 0 21 629 0 22 655 1 23 708 0 24 743 0 25 864 0 26 873 1 27 1061 0 28 1225 1 29 1257 0 30 1659 1 31 2137 1 32 2188 1 33 2441 1 34 2591 1 35 2842 0 36 2867 0 37 2880 1 38 3509 0 39 4864 1 40 5090 0 TEST FOR EXPONENTIAL within Weibulls - YOURNAME 2 S, LS, AND LLS PLOTS 12:42 Thursday, October 13, 2005 The LIFETEST Procedure Summary of the Number of Censored and Uncensored Values Percent Total Failed Censored Censored 40 29 11 27.50 TEST FOR EXPONENTIAL within Weibulls - YOURNAME 3 S, LS, AND LLS PLOTS 12:42 Thursday, October 13, 2005 The LIFETEST Procedure Survival Function Estimates S SDF | u 1.00 +A r |AA v | A i | A v | AA a 0.75 + A l | AA | A-A D | A-A i | A s 0.50 + AA t | AAA r | A--A-A i | A------------------A b | A u 0.25 + A-------A t | | i | A------------------A o | | n | | 0.00 + A F | u -+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ n 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 c days TEST FOR EXPONENTIAL within Weibulls - YOURNAME 4 S, LS, AND LLS PLOTS 12:42 Thursday, October 13, 2005 The LIFETEST Procedure Censored Observations Strata A + A A A A A AA A A A A ---+----+----+----+----+----+----+----+----+----+----+----+-- 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 days TEST FOR EXPONENTIAL within Weibulls - YOURNAME 5 S, LS, AND LLS PLOTS 12:42 Thursday, October 13, 2005 The LIFETEST Procedure -Log(Survival Function) Estimates -LOG SDF | 2.0 + | A N | ++ e | + g | ++ a 1.5 + A t | + i | + v | +++A e | ++++++++ 1.0 + +A+A+++ L | +A o | A g | A | +A S 0.5 + A D | AA F | AA | A | A 0.0 + A | ----+----+----+----+----+----+----+----+----+----+----+----+---- 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 days TEST FOR EXPONENTIAL within Weibulls - YOURNAME 6 S, LS, AND LLS PLOTS 12:42 Thursday, October 13, 2005 The LIFETEST Procedure Log(-Log(Survival Function)) Estimates L(-L(S)) | L 2 + o | g | | N | e | A g | ++A a 0 + A+AA+++ t | AA i | AA v | A+A++A e | AAA | A+++A L | +A+A o -2 + A g | +++A | +A++ S | A+ D | ++ F | + | A -4 + ----+------+------+------+------+------+------+------+------+--- 1 2 3 4 5 6 7 8 9 Log days TEST FOR EXPONENTIAL within Weibulls - YOURNAME 7 USE PROC LIFEREG TO FIT A WEIBULL DISTRIBUTION 12:42 Thursday, October 13, 2005 The LIFEREG Procedure Model Information Data Set WORK.LR1SAMP Dependent Variable Log(days) Censoring Variable status Censoring Value(s) 1 Number of Observations 40 Noncensored Values 29 Right Censored Values 11 Left Censored Values 0 Interval Censored Values 0 Name of Distribution Weibull Log Likelihood -73.00516688 Number of Observations Read 40 Number of Observations Used 40 Algorithm converged. Analysis of Parameter Estimates Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 7.2958 0.3053 6.6973 7.8942 570.98 <.0001 Scale 1 1.6440 0.2545 1.2138 2.2267 Weibull Scale 1 1474.048 450.0618 810.2510 2681.660 Weibull Shape 1 0.6083 0.0942 0.4491 0.8239 TEST FOR EXPONENTIAL within Weibulls - YOURNAME 8 NOW FIT AN EXPONENTIAL DISTRIBUTION 12:42 Thursday, October 13, 2005 Not only is there a P-value for H_0:Exponential, but you can use the difference in log likelihoods to compute the P-value of the standard nested LR hypothesis test The LIFEREG Procedure Model Information Data Set WORK.LR1SAMP Dependent Variable Log(days) Censoring Variable status Censoring Value(s) 1 Number of Observations 40 Noncensored Values 29 Right Censored Values 11 Left Censored Values 0 Interval Censored Values 0 Name of Distribution Exponential Log Likelihood -79.49623332 Number of Observations Read 40 Number of Observations Used 40 Algorithm converged. Analysis of Parameter Estimates Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 7.3597 0.1857 6.9957 7.7236 1570.78 <.0001 Scale 0 1.0000 0.0000 1.0000 1.0000 Weibull Scale 1 1571.310 291.7850 1091.938 2261.133 Weibull Shape 0 1.0000 0.0000 1.0000 1.0000 Lagrange Multiplier Statistics Parameter Chi-Square Pr > ChiSq Scale 7.8779 0.0050