NeuDist (version 1.0.1)

HLIW: Half-Logistic Inverted Weibull (HLIW) Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Half-Logistic Inverted Weibull distribution.

Usage

dHL.inv.weib(x, alpha, beta, lambda, log = FALSE)
pHL.inv.weib(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qHL.inv.weib(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rHL.inv.weib(n, alpha, beta, lambda)
hHL.inv.weib(x, alpha, beta, lambda)

Value

• dHL.inv.weib: numeric vector of (log-)densities

• pHL.inv.weib: numeric vector of probabilities

• qHL.inv.weib: numeric vector of quantiles

• rHL.inv.weib: numeric vector of random variates

• hHL.inv.weib: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric shape parameter

beta

positive numeric rate parameter

lambda

positive numeric shape parameter

log

logical; if TRUE, returns log-density

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).

log.p

logical; if TRUE, probabilities are given as log(p)

p

numeric vector of probabilities (0 < p < 1)

n

number of observations (integer > 0)

Details

The HLIW distribution is parameterized by shape parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Half-Logistic Inverted Weibull (HLIW) distribution has CDF:

$$ F(x; \alpha, \beta, \lambda) = \frac{1-\left\{1-e^{-\alpha x^{-\beta}}\right\}^\lambda} {1+\left\{1-e^{-\alpha x^{-\beta}}\right\}^\lambda} \, ; \quad x > 0. $$

where \(\alpha\), \(\beta\), and \(\lambda\) are the parameters.

The implementation includes the following functions:

• dHL.inv.weib() — Density function

• pHL.inv.weib() — Distribution function

• qHL.inv.weib() — Quantile function

• rHL.inv.weib() — Random generation

• hHL.inv.weib() — Hazard function

References

Elgarhy, M., ul Haq, M.A. & Perveen, I. (2019). Type II Half Logistic Exponential Distribution with Applications. Ann. Data. Sci., 6, 245--257 tools:::Rd_expr_doi("10.1007/s40745-018-0175-y")

Chaudhary, A. K., & Kumar, V. (2020). Half Logistic Exponential Extension Distribution with Properties and Applications. International Journal of Recent Technology and Engineering (IJRTE), 8(3), 506--512. tools:::Rd_expr_doi("10.35940/ijrte.C4625.099320")

Dhungana, G.P. & Kumar, V.(2022). Half Logistic Inverted Weibull Distribution: Properties and Applications. J. Stat. Appl. Pro. Lett., 9(3), 161--178. tools:::Rd_expr_doi("10.18576/jsapl/090306")

Examples

x <- seq(0.1, 5, 0.1)
dHL.inv.weib(x, 1.5, 0.8, 2)
pHL.inv.weib(x, 1.5, 0.8, 2)
qHL.inv.weib(0.5, 1.5, 0.8, 2)
rHL.inv.weib(10, 1.5, 0.8, 2)
hHL.inv.weib(x, 1.5, 0.8, 2)

#Data
x <- survtimes
gofic(x,
      params = list(alpha=31.1650, beta=0.4213, lambda=45.5485),
      dfun = dHL.inv.weib, pfun = pHL.inv.weib, plot=TRUE, verbose = TRUE)

pp.plot(x,
        params = list(alpha=31.1650, beta=0.4213, lambda=45.5485),
        pfun = pHL.inv.weib, fit.line=TRUE)

qq.plot(x,
        params = list(alpha=31.1650, beta=0.4213, lambda=45.5485),
        qfun = qHL.inv.weib, fit.line=TRUE)