BurrX: The BurrX (Generalized Rayleigh) distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the BurrX distribution with shape parameter alpha and scale parameter lambda.

Usage

dburrX(x, alpha, lambda, log = FALSE)
pburrX(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qburrX(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rburrX(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 BurrX distribution has density

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

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

Value

dburrX gives the density, pburrX gives the distribution function, qburrX gives the quantile function, and rburrX generates random deviates.

References

Kundu, D., and Raqab, M.Z. (2005). Generalized Rayleigh Distribution: Different Methods of Estimation, Computational Statistics and Data Analysis, 49, 187-200.

Surles, J.G., and Padgett, W.J. (2005). Some properties of a scaled Burr type X distribution, Journal of Statistical Planning and Inference, 128, 271-280.

Raqab, M.Z., and Kundu, D. (2006). Burr Type X distribution: revisited, Journal of Probability and Statistical Sciences, 4(2), 179-193.

See Also

.Random.seed about random number; sburrX for BurrX 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 = 1.1989515, lambda.est = 0.0130847

dburrX(bearings, 1.1989515, 0.0130847, log = FALSE)
pburrX(bearings, 1.1989515, 0.0130847, lower.tail = TRUE, log.p = FALSE)
qburrX(0.25, 1.1989515, 0.0130847, lower.tail=TRUE, log.p = FALSE)
rburrX(30, 1.1989515, 0.0130847)

Example output

 [1] 0.0038777276 0.0068917037 0.0079039897 0.0096729993 0.0097765895
 [6] 0.0103169195 0.0107194255 0.0110156782 0.0110256373 0.0111823805
[11] 0.0112632724 0.0112282929 0.0111822963 0.0111822963 0.0111682314
[16] 0.0095844451 0.0082307904 0.0073424782 0.0062991305 0.0061850625
[21] 0.0031489883 0.0031356221 0.0004132592
 [1] 0.02972028 0.08936313 0.11957600 0.19482875 0.20066378 0.23565681
 [7] 0.26933953 0.30239830 0.30372078 0.32771311 0.34387623 0.48279491
[13] 0.49220771 0.49220771 0.49488979 0.65456450 0.73486717 0.77785773
[19] 0.82204504 0.82653931 0.92765441 0.92803149 0.99303585
[1] 46.97775
 [1]  66.64858  14.96179  37.93952  59.97154  45.00195  76.38246  74.35418
 [8]  50.60273  85.37091  74.09369  36.52619  58.11096  72.25200  54.26715
[15]  49.60617  67.30732  79.78970  49.44015  46.68940  89.00640  16.40778
[22]  35.89981 124.48623  47.30289  48.51448  72.48315  78.38149 129.11603
[29]  48.00490 180.38325

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