NeuDist (version 1.0.1)

HLNHE: Half-Logistic NHE(Nadarajah-Haghighi Exponential) Distribution

Description

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

Usage

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

Value

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

• pHL.nhe: numeric vector of probabilities

• qHL.nhe: numeric vector of quantiles

• rHL.nhe: numeric vector of random variates

• hHL.nhe: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric parameter

beta

positive numeric parameter

lambda

positive numeric 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 Half-Logistic NHE distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Half-Logistic NHE distribution has CDF:

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

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

The functions available are listed below:

• dHL.nhe() — Density function

• pHL.nhe() — Distribution function

• qHL.nhe() — Quantile function

• rHL.nhe() — Random generation

• hHL.nhe() — Hazard function

References

Almarashi, A. M., Elgarhy, M., Elsehetry, M. M., Kibria, B. G., & Algarni, A. (2019). A new extension of exponential distribution with statistical properties and applications. Journal of Nonlinear Sciences and Applications, 12, 135--145.

Chaudhary, A.K., & Kumar, V.(2020). Half Logistic Modified Exponential Distribution:Properties and Applications. EPRA International Journal of Multidisciplinary Research (IJMR), 6(12),276--286. tools:::Rd_expr_doi("10.36713/epra3291")

Joshi, R. K., & Kumar, V. (2020). Half Logistic NHE: Properties and Application. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(9), 742--753. tools:::Rd_expr_doi("10.22214/ijraset.2020.31557")

Nadarajah, S., & Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543--558.

Examples

x <- seq(0.1, 1, 0.1)
dHL.nhe(x, 1.5, 0.8, 2)
pHL.nhe(x, 1.5, 0.8, 2)
qHL.nhe(0.5, 1.5, 0.8, 2)
rHL.nhe(10, 1.5, 0.8, 2)
hHL.nhe(x, 1.5, 0.8, 2)

#Data
x <- windshield
#ML Estimates    
params = list(alpha =0.1649, beta=3.7152, lambda=0.5881)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pHL.nhe, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qHL.nhe, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dHL.nhe, pfun = pHL.nhe, plot=FALSE)
print.gofic(out)