LogisExp: The Logistic-Exponential(LE) distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the Logistic-Exponential(LE) distribution with shape parameter alpha and scale parameter lambda.

Usage

dlogis.exp(x, alpha, lambda, log = FALSE)
plogis.exp(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qlogis.exp(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rlogis.exp(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	scale 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 Logistic-Exponential(LE) distribution has density

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

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

Value

dlogis.exp gives the density, plogis.exp gives the distribution function, qlogis.exp gives the quantile function, and rlogis.exp generates random deviates.

References

Lan, Y. and Leemis, L. M. (2008). The Logistic-Exponential Survival Distribution, Naval Research Logistics, 55, 252-264.

See Also

.Random.seed about random number; slogis.exp for ExpExt survival / hazard etc. functions

Examples

## Load data sets
data(bearings)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(bearings)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 2.36754, lambda.est = 0.01059
dlogis.exp(bearings, 2.36754, 0.01059, log = FALSE)
plogis.exp(bearings, 2.36754, 0.01059, lower.tail = TRUE, log.p = FALSE)
qlogis.exp(0.25, 2.36754, 0.01059, lower.tail=TRUE, log.p = FALSE)
rlogis.exp(30, 2.36754, 0.01059)

Example output

 [1] 0.0033823124 0.0070692981 0.0085013776 0.0111439270 0.0112987869
 [6] 0.0120879111 0.0126325050 0.0129765563 0.0129866023 0.0131216453
[11] 0.0131640653 0.0121945006 0.0120587947 0.0120587947 0.0120188415
[16] 0.0088881892 0.0070008818 0.0059659259 0.0049009850 0.0047929239
[21] 0.0023676011 0.0023584277 0.0005600842
 [1] 0.02383936 0.08093225 0.11270976 0.19689811 0.20363118 0.24438005
 [7] 0.28398137 0.32295071 0.32450850 0.35272098 0.37165120 0.52903290
[13] 0.53921974 0.53921974 0.54210907 0.70237281 0.77372906 0.80946592
[19] 0.84458486 0.84807455 0.92418756 0.92447112 0.98085560
[1] 46.06319
 [1]  48.054662  31.139879  75.369837  97.439117  61.145055  56.121111
 [7]  59.677665 104.218248 143.714824  36.952144  63.462880   6.125662
[13]  86.821711  81.921083 124.856878  47.592557  57.962373  69.432441
[19] 100.087351  81.500143  42.347134  65.341695  60.640074  59.985724
[25]  52.065776  80.813339 148.555568  33.799777 115.218824  44.801351

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