Exponential Distribution And Survival Function

R Code- (Part-II)

#Empirical Survival Function
EmpSurFun=(1-(cumsum(x)/sum(x)))
EmpSurFun

#Generating random sample from exp. dist. for obtained Lambda
RandSamp=rexp(length(x),Lambda)

#Estimated Survival Function
EstSurFun=(1-(cumsum(RandSamp)/sum(RandSamp)))
EstSurFun

Output On R Console-(Part-II)

> #Empirical Survival Function
> EmpSurFun=(1-(cumsum(x)/sum(x)))
> EmpSurFun
 [1] 0.968988814 0.963192675 0.957839554 0.956215159 0.954996862 0.950529774
 [7] 0.944992063 0.934655001 0.918632554 0.891460848 0.869900690 0.837154354
[13] 0.827444900 0.757263632 0.731605567 0.720751652 0.700003692 0.673385757
[19] 0.670579983 0.644368147 0.642669915 0.627828848 0.620666741 0.592645919
[25] 0.580869052 0.563886735 0.562410012 0.513087459 0.500719903 0.451471185
[31] 0.434710378 0.433381327 0.408756968 0.407280245 0.386753793 0.383098904
[37] 0.371875808 0.358031528 0.337098977 0.331967364 0.303171263 0.295676893
[43] 0.279580611 0.278473068 0.264296526 0.259534094 0.259201831 0.251485953
[49] 0.229372023 0.226307823 0.195591981 0.183482852 0.174401004 0.114704471
[55] 0.091150737 0.056558497 0.029423709 0.028020822 0.014545723 0.011149260
[61] 0.008121977 0.000000000
> 
>#Generating random sample from exp. dist. for obtained Lambda
> RandSamp=rexp(length(x),Lambda)
>
> #Estimated Survival Function
> EstSurFun=(1-(cumsum(RandSamp)/sum(RandSamp)))
> EstSurFun
 [1] 0.9958836847 0.9898595271 0.9561720898 0.9332247427 0.9296837477
 [6] 0.9260998591 0.9041657200 0.8911240750 0.8783892748 0.8699581171
[11] 0.8449836190 0.8002355868 0.7978138436 0.7916362753 0.7578671796
[16] 0.7467557932 0.7448121262 0.6612652168 0.6558358106 0.6504815683
[21] 0.6234970438 0.6157943592 0.6100249797 0.6075018423 0.5894325086
[26] 0.5675929444 0.5600044489 0.5440958590 0.5421978622 0.5361511402
[31] 0.5358466889 0.5260765777 0.4684343170 0.4583108311 0.4514342332
[36] 0.4354221137 0.4326665230 0.4000027499 0.3714492975 0.3674126001
[41] 0.3512239676 0.3243834923 0.3214069877 0.3116390768 0.2979975599
[46] 0.2945687680 0.2332472205 0.2120159912 0.1866437425 0.1639607321
[51] 0.1447151586 0.1415385874 0.1397198163 0.1114864165 0.0981152822
[56] 0.0911887110 0.0679361418 0.0412507487 0.0374823271 0.0277813323
[61] 0.0004643265 0.0000000000

Conclusion-

From above obtained output we can observe the empirical as well as the estimated survival functions. It is 1 at beginning and continuously decreases to 0.

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