# 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

 ```1 2 3 4``` ```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.

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

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## 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.