LFR: The linear failure rate(LFR) distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the linear failure rate(LFR) distribution with parameters alpha and beta.

Usage

dlfr(x, alpha, beta, log = FALSE)
plfr(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qlfr(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rlfr(n, alpha, beta)

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	parameter.
beta	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 linear failure rate(LFR) distribution has density

f(x) = (α + β x) exp{-(α x + (β x^2)/2)}; x ≥ 0, α > 0, β > 0.

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

Value

dlfr gives the density, plfr gives the distribution function, qlfr gives the quantile function, and rlfr generates random deviates.

References

Bain, L.J. (1974). Analysis for the Linear Failure-Rate Life-Testing Distribution, Technometrics, 16(4), 551 - 559.

Lawless, J.F.(2003). Statistical Models and Methods for Lifetime Data, John Wiley and Sons, New York.

Sen, A. and Bhattacharya, G.K.(1995). Inference procedure for the linear failure rate mode, Journal of Statistical Planning and Inference, 46, 59-76.

See Also

.Random.seed about random number; slfr for linear failure rate(LFR) survival / hazard etc. functions

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & beta for the data(sys2)
## Estimates of alpha & beta using 'maxLik' package
## alpha.est = 1.77773e-03,  beta.est = 2.77764e-06

dlfr(sys2, 1.777673e-03, 2.777640e-06, log = FALSE)
plfr(sys2, 1.777673e-03, 2.777640e-06, lower.tail = TRUE, log.p = FALSE)
qlfr(0.25, 1.777673e-03, 2.777640e-06, lower.tail=TRUE, log.p = FALSE)
rlfr(30, 1.777673e-03, 2.777640e-06)

Example output

 [1] 0.0017757358 0.0017745697 0.0017732873 0.0017705160 0.0017646173
 [6] 0.0017630576 0.0017584366 0.0017541296 0.0017532506 0.0017519531
[11] 0.0017510462 0.0017404489 0.0017362200 0.0017248826 0.0017176977
[16] 0.0016961007 0.0016944748 0.0016910991 0.0016836584 0.0016738648
[21] 0.0016680404 0.0016364557 0.0016299163 0.0016247524 0.0016185160
[26] 0.0016101383 0.0016057394 0.0015999128 0.0015914128 0.0015812527
[31] 0.0015766000 0.0015542702 0.0015397661 0.0015359545 0.0015063412
[36] 0.0014760662 0.0014703285 0.0014533265 0.0014411548 0.0013879039
[41] 0.0013878013 0.0013847407 0.0013633576 0.0013120000 0.0013022035
[46] 0.0012901269 0.0012660803 0.0012566483 0.0012365747 0.0011391786
[51] 0.0011235476 0.0011195858 0.0010871093 0.0010705849 0.0010021459
[56] 0.0009567953 0.0009380090 0.0008951652 0.0008644532 0.0008529658
[61] 0.0008429461 0.0008308842 0.0007953377 0.0007936468 0.0007381854
[66] 0.0007340977 0.0006987760 0.0006896497 0.0006623454 0.0005864691
[71] 0.0005627484 0.0005460053 0.0004615515 0.0004397958 0.0003952455
[76] 0.0003608421 0.0003348855 0.0002959755 0.0002883676 0.0002685088
[81] 0.0002314774 0.0002220609 0.0002199863 0.0002100925 0.0002021267
[86] 0.0001731487
 [1] 0.008510498 0.013232418 0.018146216 0.027962678 0.046240126 0.050632092
 [7] 0.062834306 0.073319465 0.075371284 0.078350710 0.080399966 0.102642186
[13] 0.110795042 0.131112754 0.143041502 0.175613298 0.177901938 0.182590970
[19] 0.192647867 0.205356331 0.212658439 0.249509240 0.256646303 0.262179258
[25] 0.268746908 0.277383628 0.281837628 0.287655908 0.295985330 0.305709646
[31] 0.310083281 0.330434805 0.343136031 0.346411677 0.371055729 0.394931170
[37] 0.399321305 0.412097863 0.421041873 0.458389684 0.458459077 0.460524621
[43] 0.474732501 0.507387542 0.513400223 0.520723578 0.535025707 0.540537876
[49] 0.552094030 0.605100316 0.613178247 0.615208282 0.631592917 0.639759772
[55] 0.672444677 0.693159547 0.701534502 0.720204270 0.733233759 0.738033917
[61] 0.742188882 0.747151754 0.761534701 0.762210019 0.783926933 0.785494913
[67] 0.798862245 0.802263862 0.812315209 0.839283019 0.847430272 0.853101281
[73] 0.880716787 0.887566129 0.901255990 0.911518620 0.919082110 0.930127552
[79] 0.932245705 0.937709690 0.947642869 0.950114376 0.950655880 0.953223094
[85] 0.955271622 0.962581586
[1] 145.3299
 [1] 473.71052 218.12327 751.26545 404.09551 727.31003 389.47654 534.47797
 [8] 286.00176 188.22651 374.98223 467.98512 298.20416 524.32910  57.74579
[15] 324.99441 197.31346 656.44166 176.21887 546.49865  27.88765 236.69931
[22] 171.99003 294.17826 479.44546 159.41245 506.42717 305.53556  73.17614
[29] 174.38263 748.83932

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