EPsurvival: Survival related functions for the Exponential Power(EP)...

In reliaR: Package for some probability distributions.

Description

Conditional reliability function (crf), hazard function, hazard rate average (HRA) and survival function for the Exponential Power distribution with shape parameter alpha and scale parameter lambda.

Usage

crf.exp.power(x, t = 0, alpha, lambda)
hexp.power(x, alpha, lambda)
hra.exp.power(x, alpha, lambda)
sexp.power(x, alpha, lambda)

Arguments

x	vector of quantiles.
alpha	tilt parameter.
lambda	scale parameter.
t	age component.

Value

crf.exp.power gives the conditional reliability function (crf), hexp.power gives the hazard function, hra.exp.power gives the hazard rate average (HRA) function, and sexp.power gives the survival function for the Exponential Power distribution.

References

Chen, Z.(1999). Statistical inference about the shape parameter of the exponential power distribution, Journal :Statistical Papers, Vol. 40(4), 459-468.

Pham, H. and Lai, C.D.(2007). On recent generalizations of the Weibull distribution, IEEE Trans. on Reliability, Vol. 56(3), 454-458.

Smith, R.M. and Bain, L.J.(1975). An exponential power life-test distribution, Communications in Statistics - Simulation and Computation, Vol.4(5), 469 - 481

See Also

dexp.power for other Exponential Power distribution related functions

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## alpha.est = 0.905868898, lambda.est =  0.001531423

## Reliability indicators:

## Reliability function
sexp.power(sys2, 0.905868898, 0.001531423)

## Hazard function 
hexp.power(sys2, 0.905868898, 0.001531423)

## hazard rate average(hra)
hra.exp.power(sys2, 0.905868898, 0.001531423)

## Conditional reliability function (age component=0)
crf.exp.power(sys2, 0.00, 0.905868898, 0.001531423)

## Conditional reliability function (age component=3.0)
crf.exp.power(sys2, 3.0, 0.905868898, 0.001531423)

Example output

 [1] 0.98834935 0.98261789 0.97685504 0.96573834 0.94590701 0.94125774
 [7] 0.92851525 0.91773618 0.91564258 0.91261087 0.91053120 0.88821247
[13] 0.88013131 0.86017847 0.84856905 0.81717826 0.81498684 0.81050199
[19] 0.80090430 0.78881344 0.78188292 0.74705402 0.74033073 0.73512230
[25] 0.72894363 0.72082383 0.71663846 0.71117287 0.70335126 0.69422299
[31] 0.69011820 0.67101948 0.65909788 0.65602257 0.63287006 0.61040039
[37] 0.60626317 0.59421106 0.58576288 0.55036526 0.55029929 0.54833517
[43] 0.53480442 0.50355606 0.49777739 0.49072774 0.47692272 0.47158838
[49] 0.46037907 0.40846848 0.40047944 0.39846825 0.38218290 0.37402940
[55] 0.34114274 0.32007557 0.31150590 0.29228923 0.27878280 0.27378665
[61] 0.26945309 0.26426590 0.24916434 0.24845274 0.22544598 0.22377552
[67] 0.20948291 0.20583104 0.19500513 0.16570309 0.15677956 0.15054975
[73] 0.12001990 0.11240690 0.09716163 0.08572503 0.07730551 0.06505142
[79] 0.06271066 0.05669216 0.04585222 0.04318269 0.04259962 0.03984506
[85] 0.03765966 0.02997351
 [1] 0.002229204 0.002150715 0.002099725 0.002038384 0.001982826 0.001975067
 [7] 0.001959996 0.001952539 0.001951531 0.001950292 0.001949585 0.001948052
[13] 0.001949711 0.001957596 0.001964242 0.001988139 0.001990085 0.001994169
[19] 0.002003344 0.002015702 0.002023163 0.002064449 0.002073098 0.002079940
[25] 0.002088217 0.002099351 0.002105202 0.002112958 0.002124280 0.002137821
[31] 0.002144024 0.002173806 0.002193162 0.002198250 0.002237812 0.002278350
[37] 0.002286048 0.002308893 0.002325286 0.002397482 0.002397622 0.002401800
[43] 0.002431092 0.002502287 0.002516022 0.002533029 0.002567160 0.002580650
[49] 0.002609564 0.002754422 0.002778480 0.002784617 0.002835563 0.002861942
[55] 0.002974850 0.003053310 0.003086767 0.003165372 0.003223859 0.003246231
[61] 0.003265976 0.003290041 0.003362938 0.003366483 0.003487006 0.003496236
[67] 0.003578178 0.003600021 0.003667143 0.003869551 0.003938391 0.003988819
[73] 0.004270711 0.004352216 0.004533457 0.004689135 0.004817607 0.005031987
[79] 0.005077490 0.005202737 0.005466002 0.005540375 0.005557228 0.005640082
[85] 0.005709981 0.005992671
 [1] 0.002446566 0.002353685 0.002291293 0.002212078 0.002130690 0.002117463
 [7] 0.002088076 0.002069060 0.002065851 0.002061445 0.002058579 0.002034397
[13] 0.002028020 0.002016270 0.002011562 0.002004746 0.002004540 0.002004211
[19] 0.002003916 0.002004270 0.002004810 0.002010741 0.002012438 0.002013864
[25] 0.002015677 0.002018252 0.002019663 0.002021588 0.002024501 0.002028130
[31] 0.002029840 0.002038407 0.002044247 0.002045812 0.002058356 0.002071768
[37] 0.002074367 0.002082166 0.002087833 0.002113363 0.002113414 0.002114915
[43] 0.002125502 0.002151603 0.002156688 0.002163003 0.002175730 0.002180778
[49] 0.002191629 0.002246439 0.002255590 0.002257926 0.002277337 0.002287398
[55] 0.002330497 0.002360445 0.002373208 0.002403164 0.002425418 0.002433922
[61] 0.002441422 0.002450557 0.002478186 0.002479527 0.002525044 0.002528521
[67] 0.002559334 0.002567530 0.002592669 0.002668029 0.002693503 0.002712113
[73] 0.002815348 0.002844946 0.002910368 0.002966133 0.003011859 0.003087588
[79] 0.003103572 0.003147406 0.003238798 0.003264438 0.003270238 0.003298693
[85] 0.003322626 0.003418759
 [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
[39] 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
[77] 1 1 1 1 1 1 1 1 1 1
 [1] 0.9614356 0.9747079 0.9820138 0.9895124 0.9953748 0.9961750 0.9978229
 [8] 0.9988059 0.9989664 0.9991844 0.9993250 1.0004868 1.0007940 1.0013891
[15] 1.0016569 1.0021949 1.0022249 1.0022838 1.0023998 1.0025289 1.0025955
[22] 1.0028672 1.0029099 1.0029413 1.0029766 1.0030201 1.0030414 1.0030681
[29] 1.0031042 1.0031436 1.0031603 1.0032316 1.0032711 1.0032807 1.0033468
[36] 1.0034014 1.0034106 1.0034359 1.0034525 1.0035130 1.0035131 1.0035161
[43] 1.0035357 1.0035752 1.0035818 1.0035894 1.0036036 1.0036087 1.0036191
[50] 1.0036590 1.0036642 1.0036654 1.0036751 1.0036796 1.0036956 1.0037042
[57] 1.0037074 1.0037139 1.0037180 1.0037194 1.0037205 1.0037219 1.0037255
[64] 1.0037257 1.0037302 1.0037305 1.0037328 1.0037334 1.0037348 1.0037375
[71] 1.0037379 1.0037382 1.0037383 1.0037380 1.0037369 1.0037356 1.0037344
[78] 1.0037321 1.0037316 1.0037302 1.0037269 1.0037259 1.0037257 1.0037247
[85] 1.0037237 1.0037200

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