NeuDist (version 1.0.1)

HCChen: Half-Cauchy Chen Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Half-Cauchy Chen distribution.

Usage

dhc.chen(x, beta, lambda, theta, log = FALSE)
phc.chen(q, beta, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qhc.chen(p, beta, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rhc.chen(n, beta, lambda, theta)
hhc.chen(x, beta, lambda, theta)

Value

• dhc.chen: numeric vector of (log-)densities

• phc.chen: numeric vector of probabilities

• qhc.chen: numeric vector of quantiles

• rhc.chen: numeric vector of random variates

• hhc.chen: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

beta

positive numeric parameter

lambda

positive numeric parameter

theta

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-Cauchy Chen distribution is parameterized by the parameters \(\beta > 0\), \(\lambda > 0\), and \(\theta > 0\).

The Half-Cauchy Chen distribution has CDF:

$$ F(x; \beta, \lambda, \theta) = \quad \frac{2}{\pi }\arctan \left\{ { - \frac{\lambda }{\theta } (1 - {e^{{x^\beta }}})} \right\} \quad ;\;x > 0. $$

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

Included functions are:

• dhc.chen() — Density function

• phc.chen() — Distribution function

• qhc.chen() — Quantile function

• rhc.chen() — Random generation

• hhc.chen() — Hazard function

References

Chaudhary, A.K., Yadav, R.S., & Kumar, V.(2023). Half-Cauchy Chen Distribution with Theories and Applications. Journal of Institute of Science and Technology, 28(1), 45--55. tools:::Rd_expr_doi("10.3126/jist.v28i1.56494")

Polson, N.G., & Scott, J.G. (2012). On the half-Cauchy prior for a global scale parameter. Bayesian Analysis, 7(4), 887--902.

Telee, L.B.S., & Kumar, V.(2024). Arctan-Chen Distribution with Properties and Application. International Journal of Statistics and Reliability Engineering, 11(1), 93--100.

Examples

x <- seq(1.0, 5, 0.25)
dhc.chen(x, 2.0, 0.5, 2.5)
phc.chen(x, 2.0, 0.5, 2.5)
qhc.chen(0.5, 2.0, 0.5, 2.5)
rhc.chen(10, 2.0, 0.5, 2.5)
hhc.chen(x, 2.0, 0.5, 2.5)

# Data
x <- conductors
# ML estimates
params = list(beta=0.9753, lambda=0.0398, theta=29.0272)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = phc.chen, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
res <- gofic(x, params = params,
             dfun = dhc.chen, pfun=phc.chen, plot=FALSE)
print.gofic(res)