LindleyChen: Lindley-Chen Distribution

Description

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

Usage

dlindley.chen(x, alpha, lambda, theta, log = FALSE)
plindley.chen(q, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qlindley.chen(p, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rlindley.chen(n, alpha, lambda, theta)
hlindley.chen(x, alpha, lambda, theta)

Value

dlindley.chen: numeric vector of (log-)densities
plindley.chen: numeric vector of probabilities
qlindley.chen: numeric vector of quantiles
rlindley.chen: numeric vector of random variates
hlindley.chen: numeric vector of hazard values

Arguments

x, q: numeric vector of quantiles (x, q)
alpha: 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 Lindley-Chen distribution is parameterized by the parameters $\alpha > 0$, $\lambda > 0$, and $\theta > 0$.

The Lindley-Chen distribution has CDF:

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

where $\alpha$, $\lambda$, and $\theta$ are the parameters.

The functions available are listed below:

dlindley.chen() — Density function
plindley.chen() — Distribution function
qlindley.chen() — Quantile function
rlindley.chen() — Random generation
hlindley.chen() — Hazard function

References

Bhati, D., Malik, M. A., & Vaman, H. J. (2015). Lindley–Exponential distribution: properties and applications. Metron, 73(3), 335--357.

Joshi, R. K., & Kumar, V. (2020). Lindley-Chen Distribution with Applications. International Journal of Engineering, Science & Mathematics (IJESM), 9(10), 12--22.

Examples

Run this code

x <- seq(1.0, 3.0, 0.25)
dlindley.chen(x, 0.5, 2, 0.5)
plindley.chen(x, 0.5, 2, 0.5)
qlindley.chen(0.5, 0.5, 2, 0.5)
rlindley.chen(10, 0.5, 2, 0.5)
hlindley.chen(x, 0.5, 2, 0.5)

# Data
x <- fibers65
# ML estimates
params = list(alpha=1.26813, lambda=28.96389, theta=0.00355)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plindley.chen, fit.line=TRUE)

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

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

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