reliaR (version 0.01)

BurrX: The BurrX (Generalized Rayleigh) distribution

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

Value

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

Details

The BurrX distribution has density $$f(x; \alpha, \lambda) = 2 \alpha \lambda^2 x e^{-(\lambda x)^2} \left\{1-e^{-(\lambda x)^2} \right\}^{\alpha -1}; (\alpha, \lambda) > 0, x >0.$$ where $\alpha$ and $\lambda$ are the shape and scale parameters, respectively.

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)