# Gumbelsurvival: Survival related functions for the Gumbel distribution In reliaR: Package for some probability distributions.

## Description

Conditional reliability function (crf), hazard function, hazard rate average (HRA) and survival function for the Gumbel distribution with location parameter `mu` and scale parameter `sigma`.

## Usage

 ```1 2 3 4``` ```crf.gumbel(x, t = 0, mu, sigma) hgumbel(x, mu, sigma) hra.gumbel(x, mu, sigma) sgumbel(x, mu, sigma) ```

## Arguments

 `x` vector of quantiles. `mu` location parameter. `sigma` scale parameter. `t` age component.

## Value

`crf.gumbel` gives the conditional reliability function (crf), `hgumbel` gives the hazard function, `hra.gumbel` gives the hazard rate average (HRA) function, and `sgumbel` gives the survival function for the Gumbel distribution.

## References

Marshall, A. W., Olkin, I.(2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families, Springer, New York.

`dgumbel` for other Gumbel distribution related functions;

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```## load data set data(dataset2) ## Maximum Likelihood(ML) Estimates of mu & sigma for the data(dataset2) ## Estimates of mu & sigma using 'maxLik' package ## mu.est = 212.157, sigma.est = 151.768 ## Reliability indicators for data(dataset2): ## Reliability function sgumbel(dataset2, 212.157, 151.768) ## Hazard function hgumbel(dataset2, 212.157, 151.768) ## hazard rate average(hra) hra.gumbel(dataset2, 212.157, 151.768) ## Conditional reliability function (age component=0) crf.gumbel(dataset2, 0.00, 212.157, 151.768) ## Conditional reliability function (age component=3.0) crf.gumbel(dataset2, 3.0, 212.157, 151.768) ```

### Example output

```  [1] 0.976223654 0.974418341 0.965436041 0.956268409 0.942380779 0.942380779
[7] 0.934470710 0.934470710 0.934470710 0.930880389 0.924628393 0.924628393
[13] 0.905344166 0.891582915 0.881831970 0.881831970 0.873363574 0.871633278
[19] 0.871633278 0.869890937 0.868136622 0.861001124 0.861001124 0.853680218
[25] 0.830660148 0.828673643 0.818592770 0.760405711 0.744467062 0.742167067
[31] 0.742167067 0.725922980 0.702342145 0.688026639 0.678429360 0.676024420
[37] 0.656722035 0.651883150 0.627653311 0.591375199 0.588966437 0.576950832
[43] 0.576950832 0.572159422 0.569767246 0.569767246 0.567377537 0.557845043
[49] 0.538923349 0.534226406 0.524876831 0.517905633 0.510971590 0.504076451
[55] 0.499502137 0.492675536 0.492675536 0.490409533 0.485892163 0.474686635
[61] 0.463611822 0.454850132 0.454850132 0.448338005 0.444025378 0.431229138
[67] 0.418651384 0.412446650 0.382294060 0.382294060 0.374504910 0.372574489
[73] 0.363024354 0.357376331 0.337198659 0.333620316 0.299374136 0.267911793
[79] 0.263429533 0.261949037 0.244708119 0.237807096 0.236446589 0.236446589
[85] 0.228420131 0.205715514 0.205715514 0.205715514 0.205715514 0.198592721
[91] 0.198592721 0.184990558 0.170166578 0.169149402 0.149921291 0.131890270
[97] 0.129483718 0.125562803 0.097341531 0.096734227 0.088599936 0.081118596
[103] 0.056453966 0.056453966 0.052612771 0.032858318 0.031604986 0.025178514
[109] 0.022985508 0.005773593 0.003644187
[1] 0.0006000376 0.0006341343 0.0007937753 0.0009430524 0.0011497393
[6] 0.0011497393 0.0012592072 0.0012592072 0.0012592072 0.0013072243
[11] 0.0013885944 0.0013885944 0.0016240769 0.0017801426 0.0018856607
[16] 0.0018856607 0.0019742635 0.0019920427 0.0019920427 0.0020098385
[21] 0.0020276499 0.0020990276 0.0020990276 0.0021705617 0.0023854004
[26] 0.0024032811 0.0024925436 0.0029663666 0.0030857743 0.0031026865
[31] 0.0031026865 0.0032199735 0.0033839439 0.0034801453 0.0035433219
[36] 0.0035589933 0.0036825536 0.0037129311 0.0038616561 0.0040745909
[41] 0.0040883453 0.0041562822 0.0041562822 0.0041830665 0.0041963748
[46] 0.0041963748 0.0042096272 0.0042620777 0.0043642943 0.0043892900
[51] 0.0044386131 0.0044750223 0.0045109334 0.0045463482 0.0045696834
[56] 0.0046042759 0.0046042759 0.0046156977 0.0046383782 0.0046941334
[61] 0.0047485481 0.0047911245 0.0047911245 0.0048225049 0.0048431643
[66] 0.0049039029 0.0049628063 0.0049915800 0.0051288407 0.0051288407
[71] 0.0051636298 0.0051722106 0.0052144243 0.0052392067 0.0053266589
[76] 0.0053419949 0.0054862392 0.0056149134 0.0056329594 0.0056389047
[81] 0.0057075908 0.0057348049 0.0057401515 0.0057401515 0.0057715716
[86] 0.0058593357 0.0058593357 0.0058593357 0.0058593357 0.0058865372
[91] 0.0058865372 0.0059380548 0.0059935733 0.0059973593 0.0060683701
[96] 0.0061340197 0.0061427145 0.0061568472 0.0062573688 0.0062595092
[101] 0.0062880876 0.0063142245 0.0063994144 0.0063994144 0.0064125490
[106] 0.0064795469 0.0064837670 0.0065053485 0.0065126915 0.0065699464
[111] 0.0065769839
[1] 0.002005297 0.001727637 0.001256265 0.001146581 0.001119733 0.001119733
[7] 0.001129583 0.001129583 0.001129583 0.001136897 0.001152402 0.001152402
[13] 0.001212684 0.001261064 0.001296430 0.001296430 0.001327484 0.001333849
[19] 0.001333849 0.001340264 0.001346726 0.001373023 0.001373023 0.001399988
[25] 0.001484276 0.001491499 0.001528004 0.001733564 0.001788404 0.001796271
[31] 0.001796271 0.001851511 0.001930790 0.001978454 0.002010233 0.002018176
[37] 0.002081656 0.002097500 0.002176483 0.002293907 0.002301679 0.002340418
[43] 0.002340418 0.002355855 0.002363560 0.002363560 0.002371257 0.002401951
[49] 0.002462876 0.002478006 0.002508139 0.002530624 0.002553009 0.002575291
[55] 0.002590087 0.002612194 0.002612194 0.002619538 0.002634192 0.002670611
[61] 0.002706717 0.002735373 0.002735373 0.002756728 0.002770900 0.002813096
[67] 0.002854809 0.002875482 0.002976982 0.002976982 0.003003518 0.003010117
[73] 0.003042899 0.003062399 0.003132804 0.003145420 0.003268459 0.003385855
[79] 0.003402983 0.003408665 0.003475776 0.003503160 0.003508596 0.003508596
[85] 0.003540932 0.003635083 0.003635083 0.003635083 0.003635083 0.003665531
[91] 0.003665531 0.003725056 0.003792243 0.003796951 0.003888616 0.003979931
[97] 0.003992578 0.004013441 0.004174784 0.004178512 0.004229711 0.004279119
[103] 0.004463245 0.004463245 0.004495872 0.004691690 0.004706322 0.004787730
[109] 0.004818507 0.005185574 0.005276900
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1] 1.056824 1.055421 1.049732 1.045383 1.040406 1.040406 1.038133 1.038133
[9] 1.038133 1.037200 1.035698 1.035698 1.031822 1.029568 1.028160 1.028160
[17] 1.027041 1.026823 1.026823 1.026607 1.026393 1.025555 1.025555 1.024745
[25] 1.022477 1.022298 1.021428 1.017324 1.016405 1.016278 1.016278 1.015419
[33] 1.014277 1.013636 1.013226 1.013126 1.012352 1.012167 1.011283 1.010086
[41] 1.010011 1.009646 1.009646 1.009504 1.009434 1.009434 1.009365 1.009092
[49] 1.008572 1.008447 1.008203 1.008025 1.007851 1.007681 1.007570 1.007407
[57] 1.007407 1.007353 1.007247 1.006989 1.006741 1.006550 1.006550 1.006410
[65] 1.006318 1.006052 1.005798 1.005675 1.005101 1.005101 1.004958 1.004924
[73] 1.004753 1.004653 1.004307 1.004247 1.003693 1.003214 1.003148 1.003126
[81] 1.002878 1.002780 1.002761 1.002761 1.002650 1.002342 1.002342 1.002342
[89] 1.002342 1.002248 1.002248 1.002072 1.001883 1.001871 1.001634 1.001417
[97] 1.001389 1.001343 1.001020 1.001013 1.000922 1.000840 1.000574 1.000574
[105] 1.000534 1.000329 1.000316 1.000251 1.000228 1.000057 1.000036
```

reliaR documentation built on May 1, 2019, 9:51 p.m.