Description Usage Arguments Details Value Note Author(s) Source References See Also Examples
Density function, distribution function, quantile function, random number generation and hazard rate function for the generalized inverse Lindley distribution with parameters theta and alpha.
1 2 3 4 5 6 7 8 9 | dgenilindley(x, theta, alpha, log = FALSE)
pgenilindley(q, theta, alpha, lower.tail = TRUE, log.p = FALSE)
qgenilindley(p, theta, alpha, lower.tail = TRUE, log.p = FALSE)
rgenilindley(n, theta, alpha, mixture = TRUE)
hgenilindley(x, theta, alpha, log = TRUE)
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x, q |
vector of positive quantiles. |
theta, alpha |
positive parameters. |
log, log.p |
logical; If TRUE, probabilities p are given as log(p). |
lower.tail |
logical; If TRUE, (default), P(X ≤q x) are returned, otherwise P(X > x). |
p |
vector of probabilities. |
n |
number of observations. If |
mixture |
logical; If TRUE, (default), random deviates are generated from a two-component mixture of generalized inverse gamma distributions, otherwise from the quantile function. |
Probability density function
f(x\mid θ,α )=\frac{α θ ^{2}}{1+θ }≤ft( \frac{1+x^{α }}{x^{2α +1}}\right) e^{-\frac{θ }{x^{α }}}
Cumulative distribution function
F(x\mid θ,α )=≤ft( 1+\frac{θ }{≤ft( 1+θ \right) {x}^{α }}\right) e{{^{-{\frac{θ }{x^{α }}}}}}
Quantile function
Q(p\mid θ ,α) =≤ft( -1-\frac{1}{θ }-\frac{1}{θ }W_{-1}≤ft( -p≤ft( 1+θ \right) e{^{-(1+θ) }}\right) \right) ^{- \frac{1}{α }}
Hazard rate function
h(x\mid θ,α )={\frac{α {θ }^{2}≤ft( 1+{x}^{α}\right) e{{^{-{\frac{θ }{{x}^{α }}}}}}}{≤ft( 1+θ \right) {x}^{2α +1}≤ft[ 1-≤ft( 1+\frac{θ }{≤ft( 1+θ \right) {x}^{α }}\right) e{{^{-{\frac{θ }{x^{α }}}}}}\right] }}
where W_{-1} denotes the negative branch of the Lambert W function.
Particular case: α = 1 the inverse Lindley distribution.
dgenilindley
gives the density, pgenilindley
gives the distribution function, qgenilindley
gives the quantile function, rgenilindley
generates random deviates and hgenilindley
gives the hazard rate function.
Invalid arguments will return an error message.
Barco et al. (2016) named the generalized inverse Lindley distribution as inverse power Lindley distribution.
Josmar Mazucheli jmazucheli@gmail.com
Larissa B. Fernandes lbf.estatistica@gmail.com
[d-h-p-q-r]genilindley are calculated directly from the definitions. rgenilindley
uses either a two-component mixture of generalized inverse gamma distributions or the quantile function.
Barco, K. V. P., Mazucheli, J. and Janeiro, V. (2016). The inverse power Lindley distribution. Communications in Statistics - Simulation and Computation, (to appear).
Sharma, V. K., Singh, S. K., Singh, U., Merovci, F., (2015). The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communication in Statistics - Theory and Methods, 0, 0, 0-0.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | set.seed(1)
x <- rgenilindley(n = 1000, theta = 10, alpha = 20, mixture = TRUE)
R <- range(x)
S <- seq(from = R[1], to = R[2], by = 0.01)
plot(S, dgenilindley(S, theta = 10, alpha = 20), xlab = 'x', ylab = 'pdf')
hist(x, prob = TRUE, main = '', add = TRUE)
p <- seq(from = 0.1, to = 0.9, by = 0.1)
q <- quantile(x, prob = p)
pgenilindley(q, theta = 10, alpha = 20, lower.tail = TRUE)
pgenilindley(q, theta = 10, alpha = 20, lower.tail = FALSE)
qgenilindley(p, theta = 10, alpha = 20, lower.tail = TRUE)
qgenilindley(p, theta = 10, alpha = 20, lower.tail = FALSE)
library(fitdistrplus)
fit <- fitdist(x, 'genilindley', start = list(theta = 10, alpha = 20))
plot(fit)
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