Description Usage Arguments Details Value Author(s) Source References See Also Examples
Density function, distribution function, quantile function, random number generation and hazard rate function for the Lindley exponential distribution with parameters theta and alpha.
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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 |
Probability density function
f(x\mid θ ,α )={\frac{{θ }^{2}α {{e}^{-α x}}≤ft(1-{{e}^{-α x}}\right) ^{θ -1}≤ft[ 1-\log ≤ft( 1-{{e}^{-α x}}\right) \right] }{1+θ }}
Cumulative distribution function
F(x\mid θ ,α )={\frac{≤ft( 1-{{e}^{-α x}}\right) ^{θ }≤ft[ 1+θ -θ \log ≤ft( 1-{{e}^{-α x}}\right) \right] }{1+θ }}
Quantile function
\code{see Bhati et al., 2015}
Hazard rate function
\code{see Bhati et al., 2015}
dlindleye
gives the density, plindleye
gives the distribution function, qlindleye
gives the quantile function, rlindleye
generates random deviates and hlindleye
gives the hazard rate function.
Invalid arguments will return an error message.
Josmar Mazucheli jmazucheli@gmail.com
Larissa B. Fernandes lbf.estatistica@gmail.com
[d-h-p-q-r]lindleye are calculated directly from the definitions. rlindleye
uses the quantile function.
Bhati, D., Malik, M. A., Vaman, H. J., (2015). Lindley-Exponential distribution: properties and applications. METRON, 73, (3), 335–357.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | set.seed(1)
x <- rlindleye(n = 1000, theta = 5.0, alpha = 0.2)
R <- range(x)
S <- seq(from = R[1], to = R[2], by = 0.1)
plot(S, dlindleye(S, theta = 5.0, alpha = 0.2), 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)
plindleye(q, theta = 5.0, alpha = 0.2, lower.tail = TRUE)
plindleye(q, theta = 5.0, alpha = 0.2, lower.tail = FALSE)
qlindleye(p, theta = 5.0, alpha = 0.2, lower.tail = TRUE)
qlindleye(p, theta = 5.0, alpha = 0.2, lower.tail = FALSE)
## waiting times data (from Ghitany et al., 2008)
data(waitingtimes)
library(fitdistrplus)
fit <- fitdist(waitingtimes, 'lindleye', start = list(theta = 2.6, alpha = 0.15),
lower = c(0.01, 0.01))
plot(fit)
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