MOEW: The Marshall-Olkin Extended Weibull (MOEW) distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the Marshall-Olkin Extended Weibull (MOEW) distribution with tilt parameter alpha and scale parameter lambda.

Usage

dmoew(x, alpha, lambda, log = FALSE)
pmoew(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qmoew(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rmoew(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	tilt 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 Marshall-Olkin extended Weibull (MOEW) distribution has density

f(x) = {λ α x^{α - 1} exp(-x^α)} / {{1 - (1 - λ) \exp(-x^α)}^2}; x > 0, λ > 0, α > 0

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

Value

dmoew gives the density, pmoew gives the distribution function, qmoew gives the quantile function, and rmoew generates random deviates.

References

Marshall, A. W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the Weibull and Weibull families. Biometrika,84(3):641-652.

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

See Also

.Random.seed about random number; smoew for MOEW survival / hazard etc. functions;

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## alpha.est = 0.3035937,  lambda.est = 279.2177754

dmoew(sys2, 0.3035937, 279.2177754, log = FALSE)
pmoew(sys2, 0.3035937, 279.2177754, lower.tail = TRUE, log.p = FALSE)
qmoew(0.25, 0.3035937, 279.2177754, lower.tail=TRUE, log.p = FALSE)
rmoew(50, 0.3035937, 279.2177754)

Example output

 [1] 0.0017740880 0.0016281327 0.0015583356 0.0015056205 0.0015036471
 [6] 0.0015099247 0.0015327819 0.0015556915 0.0015603354 0.0015671261
[11] 0.0015718177 0.0016221608 0.0016397212 0.0016800334 0.0017010115
[16] 0.0017468850 0.0017494548 0.0017544473 0.0017639171 0.0017734680
[21] 0.0017777405 0.0017860199 0.0017851250 0.0017838905 0.0017818207
[26] 0.0017781164 0.0017757771 0.0017722889 0.0017664575 0.0017584307
[31] 0.0017544024 0.0017323747 0.0017160090 0.0017114769 0.0016735093
[36] 0.0016307006 0.0016222377 0.0015966366 0.0015778963 0.0014931788
[41] 0.0014930127 0.0014880534 0.0014532617 0.0013693599 0.0013534017
[46] 0.0013337820 0.0012949435 0.0012798096 0.0012478223 0.0010980002
[51] 0.0010749146 0.0010691090 0.0010222275 0.0009988670 0.0009057313
[56] 0.0008472425 0.0008237621 0.0007718294 0.0007359616 0.0007228322
[61] 0.0007115058 0.0006980248 0.0006592591 0.0006574503 0.0005998507
[66] 0.0005957353 0.0005608932 0.0005520965 0.0005262695 0.0004581916
[71] 0.0004379641 0.0004239734 0.0003568001 0.0003403540 0.0003076740
[76] 0.0002832888 0.0002653392 0.0002390814 0.0002340300 0.0002209589
[81] 0.0001969678 0.0001909325 0.0001896057 0.0001832913 0.0001782208
[86] 0.0001598370
 [1] 0.01411511 0.01861270 0.02301456 0.03146902 0.04697223 0.05072383
 [7] 0.06126334 0.07048159 0.07230446 0.07496280 0.07679908 0.09714745
[13] 0.10479685 0.12428933 0.13600593 0.16892711 0.17128715 0.17614014
[19] 0.18662572 0.20001646 0.20777618 0.24755313 0.25535637 0.26142383
[25] 0.26864461 0.27816793 0.28309014 0.28953002 0.29876656 0.30957098
[31] 0.31443631 0.33710577 0.35126261 0.35491291 0.38233931 0.40879581
[37] 0.41364272 0.42771002 0.43751958 0.47807234 0.47814699 0.48036789
[43] 0.49557502 0.53002875 0.53629111 0.54388241 0.55859006 0.56421588
[49] 0.57593132 0.62823540 0.63599253 0.63793287 0.65345936 0.66110897
[55] 0.69112630 0.70965827 0.71704369 0.73328965 0.74445289 0.74853012
[61] 0.75204418 0.75622331 0.76822531 0.76878492 0.78660096 0.78787426
[67] 0.79866225 0.80138902 0.80940507 0.83064314 0.83699572 0.84140410
[73] 0.86277788 0.86807515 0.87869590 0.88671601 0.89267991 0.90151072
[79] 0.90322567 0.90768997 0.91599403 0.91810789 0.91857405 0.92079999
[85] 0.92259657 0.92918448
[1] 146.4001
 [1]  131.80429  205.71750  671.81718   85.25697   29.66341  685.46278
 [7]   13.39062  226.26649   96.69232  314.15236  412.73650  668.81192
[13]   53.97690  112.11491  396.86386  271.56845  332.20093   77.01324
[19]  221.35589  499.49443  358.57376  508.27565  420.15996   11.22592
[25]  355.01044  150.85920  201.99224  295.40742  304.01218  992.43779
[31]  525.24908  198.16964   32.47047  651.46052  203.36411  107.85350
[37]  170.15368  283.60068   49.08322   50.40690  368.95876  560.19840
[43]  273.94321  574.80760  300.13962  990.11700   93.09721  628.84056
[49] 2610.31839   16.09373

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