NeuDist (version 1.0.1)

LogisNHE: Logistic-NHE Distribution

Description

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

Usage

dlogis.NHE(x, alpha, beta, lambda, log = FALSE)
plogis.NHE(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qlogis.NHE(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rlogis.NHE(n, alpha, beta, lambda)
hlogis.NHE(x, alpha, beta, lambda)

Value

• dlogis.NHE: numeric vector of (log-)densities

• plogis.NHE: numeric vector of probabilities

• qlogis.NHE: numeric vector of quantiles

• rlogis.NHE: numeric vector of random variates

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

The Logistic-NHE distribution has CDF:

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

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

Included functions are:

• dlogis.NHE() — Density function

• plogis.NHE() — Distribution function

• qlogis.NHE() — Quantile function

• rlogis.NHE() — Random generation

• hlogis.NHE() — Hazard function

References

Chaudhary,A.K., & Kumar, V.(2020). The Logistic NHE Distribution with Properties and Applications. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(12),591--603. tools:::Rd_expr_doi("10.22214/ijraset.2020.32565")

Examples

x <- seq(0.1, 2.0, 0.2)
dlogis.NHE(x, 2.0, 5.0, 0.2)
plogis.NHE(x, 2.0, 5.0, 0.1)
qlogis.NHE(0.5, 2.0, 5.0, 0.1)
rlogis.NHE(10, 2.0, 5.0, 0.1)
hlogis.NHE(x, 2.0, 5.0, 0.1)

# Data
x <- conductors
# ML estimates
params = list(alpha=4.39078, beta=6.98955, lambda=0.01133)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.NHE, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dlogis.NHE, pfun=plogis.NHE, plot=TRUE)
print.gofic(out)