NeuDist (version 1.0.1)

ChenExp: Chen-Exponential Distribution

Description

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

Usage

dchen.exp(x, alpha, beta, lambda, log = FALSE)
pchen.exp(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qchen.exp(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rchen.exp(n, alpha, beta, lambda)
hchen.exp(x, alpha, beta, lambda)

Value

• dchen.exp: numeric vector of (log-)densities

• pchen.exp: numeric vector of probabilities

• qchen.exp: numeric vector of quantiles

• rchen.exp: numeric vector of random variates

• hchen.exp: 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 Chen-Exponential distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Chen-Exponential distribution has CDF:

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

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

The following functions are included:

• dchen.exp() — Density function

• pchen.exp() — Distribution function

• qchen.exp() — Quantile function

• rchen.exp() — Random generation

• hchen.exp() — Hazard function

References

Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49, 155--161.

Sapkota, L.P., & Kumar, V. (2023). Chen Exponential Distribution with Applications to Engineering Data. International Journal of Statistics and Reliability Engineering, 10(1), 33--47.

Sapkota, L.P., Alsahangiti, A.M., Kumar, V. Gemeay, A.M., Bakr, M.E., Balogun, O.S., & Muse, A.H. (2023). Arc-Tangent Exponential Distribution With Applications to Weather and Chemical Data Under Classical and Bayesian Approach, IEEE Access, 11, 115462--115476. tools:::Rd_expr_doi("10.1109/ACCESS.2023.3324293")

Examples

x <- seq(0.1, 1, 0.1)
dchen.exp(x, 1.5, 0.8, 2)
pchen.exp(x, 1.5, 0.8, 2)
qchen.exp(0.5, 1.5, 0.8, 2)
rchen.exp(10, 1.5, 0.8, 2)
hchen.exp(x, 1.5, 0.8, 2)
#Data
x <- stress
#ML Estimates    
params = list(alpha=2.5462, beta=0.0537, lambda=87.6028)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pchen.exp, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
# Display plot; numerical summary stored in 'out'
out <- gofic(x, params = params, dfun = dchen.exp, 
             pfun = pchen.exp, plot=TRUE)
print.gofic(out)