ExpExt: The Exponential Extension(EE) distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the Exponential Extension(EE) distribution with shape parameter alpha and scale parameter lambda.

Usage

dexp.ext(x, alpha, lambda, log = FALSE)
pexp.ext(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qexp.ext(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rexp.ext(n, alpha, lambda)

Arguments

x,q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
alpha	shape parameter.
lambda	scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].

Details

The Exponential Extension(EE) distribution has density

f(x) = α λ (1 + λ x)^{α - 1} exp(1 - (1 + λ x)^α); x ≥ 0, α > 0, λ > 0.

where α and λ are the shape and scale parameters, respectively.

Value

dexp.ext gives the density, pexp.ext gives the distribution function, qexp.ext gives the quantile function, and rexp.ext generates random deviates.

References

Nikulin, M. and Haghighi, F. (2006). A Chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data, Journal of Mathematical Sciences, Vol. 133(3), 1333-1341.

See Also

.Random.seed about random number; sexp.ext for ExpExt survival / hazard etc. functions

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 1.0126e+01, lambda.est = 1.5848e-04
dexp.ext(sys2, 1.012556e+01, 1.5848e-04, log = FALSE)
pexp.ext(sys2, 1.012556e+01, 1.5848e-04, lower.tail = TRUE, log.p = FALSE)
qexp.ext(0.25, 1.012556e+01, 1.5848e-04, lower.tail=TRUE, log.p = FALSE)
rexp.ext(30, 1.012556e+01, 1.5848e-04)

Example output

 [1] 0.0016034341 0.0016026915 0.0016018876 0.0016001859 0.0015966736
 [6] 0.0015957622 0.0015930911 0.0015906310 0.0015901316 0.0015893959
[11] 0.0015888826 0.0015829253 0.0015805623 0.0015742454 0.0015702469
[16] 0.0015582024 0.0015572926 0.0015554022 0.0015512263 0.0015457092
[21] 0.0015424159 0.0015243792 0.0015206044 0.0015176134 0.0015139889
[26] 0.0015090983 0.0015065204 0.0015030951 0.0014980759 0.0014920416
[31] 0.0014892654 0.0014758276 0.0014669969 0.0014646626 0.0014463334
[36] 0.0014272340 0.0014235726 0.0014126447 0.0014047486 0.0013694814
[41] 0.0013694123 0.0013673491 0.0013528232 0.0013171336 0.0013101955
[46] 0.0013015846 0.0012842465 0.0012773754 0.0012626189 0.0011883935
[51] 0.0011760662 0.0011729231 0.0011468722 0.0011334196 0.0010762535
[56] 0.0010370553 0.0010205022 0.0009820466 0.0009538664 0.0009431923
[61] 0.0009338219 0.0009224668 0.0008885237 0.0008868910 0.0008324184
[66] 0.0008283320 0.0007926056 0.0007832525 0.0007549669 0.0006739418
[71] 0.0006478698 0.0006292521 0.0005326264 0.0005070053 0.0004536306
[76] 0.0004116084 0.0003794694 0.0003306636 0.0003210427 0.0002958279
[81] 0.0002485122 0.0002364447 0.0002337852 0.0002211026 0.0002108954
[86] 0.0001738793
 [1] 0.007683515 0.011947669 0.016386018 0.025255819 0.041783961 0.045758549
 [7] 0.056808040 0.066311524 0.068172271 0.070874871 0.072734165 0.092939296
[13] 0.100357710 0.118876994 0.129772775 0.159620597 0.161723557 0.166034646
[19] 0.175292473 0.187014524 0.193762106 0.227960689 0.234614006 0.239778990
[25] 0.245918007 0.254004818 0.258181457 0.263643925 0.271477029 0.280641817
[31] 0.284770934 0.304044766 0.316125241 0.319247462 0.342827899 0.365832098
[37] 0.370079808 0.382474283 0.391180099 0.427805344 0.427873817 0.429912705
[43] 0.443976307 0.476567048 0.482609930 0.489988254 0.504456327 0.510053491
[49] 0.521826553 0.576527479 0.584968668 0.587094504 0.604319557 0.612950533
[55] 0.647801553 0.670150870 0.679245341 0.699641979 0.713977609 0.719279897
[61] 0.723878586 0.729382490 0.745400821 0.746155372 0.770535043 0.772303742
[67] 0.787426858 0.791287705 0.802724168 0.833595451 0.842966747 0.849499082
[73] 0.881365390 0.889265909 0.905017662 0.916762986 0.925363452 0.937797547
[79] 0.940159883 0.946212464 0.957025157 0.959667822 0.960243850 0.962959071
[85] 0.965105838 0.972597073
[1] 159.5484
 [1]  76.18151 533.79438 550.34297 308.21254 317.17397 417.21090 671.92179
 [8] 973.64593 685.79557 443.02469 111.63522  59.56529 325.51133 456.37737
[15] 350.42036 153.00333 557.08346 216.91177 558.21764 993.05607 416.99768
[22] 326.19418 598.37114 183.01135 237.91066 891.16401 201.37094 100.89105
[29]  56.91061 152.94923

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