ModAtanExp: Modified Atan Exponential Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Modified Atan Exponential distribution.

Usage

dmod.atan.exp(x, alpha, beta, lambda, log = FALSE)
pmod.atan.exp(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qmod.atan.exp(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rmod.atan.exp(n, alpha, beta, lambda)
hmod.atan.exp(x, alpha, beta, lambda)

Value

dmod.atan.exp: numeric vector of (log-)densities
pmod.atan.exp: numeric vector of probabilities
qmod.atan.exp: numeric vector of quantiles
rmod.atan.exp: numeric vector of random variates
hmod.atan.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 Modified Atan Exponential distribution is parameterized by the parameters $\alpha > 0$, $\beta > 0$, and $\lambda > 0$.

The Modified Atan Exponential distribution has CDF:

$$ F(x; \alpha, \beta, \lambda) = \left[\frac{2}{\pi} \arctan \left\{\beta x e^{\alpha x}\right\}\right] ^\lambda ; x \geq 0. $$

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

The following functions are included:

dmod.atan.exp() — Density function
pmod.atan.exp() — Distribution function
qmod.atan.exp() — Quantile function
rmod.atan.exp() — Random generation
hmod.atan.exp() — Hazard function

References

Chaudhary, A.K., Telee, L.B.S., & Kumar, V.(2023). Modified Arctan Exponential Distribution with application to COVID-19 Second Wave data in Nepal. Journal of Econometrics and Statistics, 4(1), 63--78.

Examples

Run this code

x <- seq(0.1, 10, 0.2)
dmod.atan.exp(x, 0.1, 0.2, 1.2)
pmod.atan.exp(x, 0.1, 0.2, 1.2)
qmod.atan.exp(0.5, 0.1, 0.2, 1.2)
rmod.atan.exp(10, 0.1, 0.2, 1.2)
hmod.atan.exp(x, 0.1, 0.2, 1.2)

# Data
x <- bladder
# ML estimates
params = list(alpha=0.04599, beta=0.14935, lambda=1.23266)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pmod.atan.exp, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dmod.atan.exp, pfun=pmod.atan.exp, plot=FALSE)
print.gofic(out)

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