LFR: The linear failure rate(LFR) distribution

In reliaR: Comprehensive Tools for some Probability Distributions

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].

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.

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)

reliaR documentation built on Nov. 5, 2025, 6:57 p.m.