reliaR (version 0.01)

LFR: The linear failure rate(LFR) distribution

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 $P[X \le x]$ otherwise, $P[X > x]$.

Value

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

Details

The linear failure rate(LFR) distribution has density $$f(x) = \left(\alpha + \beta x\right)\; \exp\left\{-\left(\alpha x + \frac{\beta x^2}{2}\right)\right\};\, x \ge 0, \alpha > 0, \beta > 0.$$ where $\alpha$ and $\beta$ are the shape and scale parameters, respectively.

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)