Description Usage Arguments Details Value Author(s) Source References See Also Examples
Probability mass function, distribution function, quantile function and random number generation for the discrete weighted Lindley distribution with parameters theta and alpha.
1 2 3 4 5 6 7 | ddwlindley(x, theta, alpha, log = FALSE)
pdwlindley(q, theta, alpha, lower.tail = TRUE, log.p = FALSE)
qdwlindley(p, theta, alpha, lower.tail = TRUE, log.p = FALSE)
rdwlindley(n, theta, alpha)
|
x, q |
vector of integer positive quantiles. |
theta, alpha |
positive parameter. |
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 mass function
P(X=x\mid θ ,α )=\frac{1}{≤ft( θ +α \right) Γ ≤ft( α \right) }∑\limits_{i=0}^{1}≤ft( -1\right) ^{i}≤ft\{ ≤ft( θ +α \right) Γ ≤ft[ α ,θ ≤ft( x+i\right) \right] +≤ft[θ ≤ft( x+i\right) \right] ^{α }e^{-θ ≤ft( x+i\right)}\right\}
where Γ ≤ft(α,θ x\right) = \int_{θ x}^{∞}x^{α -1}e^{-x}dx is the upper incomplete gamma function.
Particular case: α = 1 the one-parameter discrete Lindley distribution.
ddwlindley
gives the probability mass function, pdwlindley
gives the distribution function, qdwlindley
gives the quantile function and rdwlindley
generates random deviates.
Invalid arguments will return an error message.
Josmar Mazucheli jmazucheli@gmail.com
Ricardo P. de Oliveira rpuziol.oliveira@gmail.com
[d-p-q-r]dwlindley are calculated directly from the definitions. rdwlindley
uses the discretize values.
Al-Mutairi, D. K., Ghitany, M. E., Kundu, D., (2015). Inferences on stress-strength reliability from weighted Lindley distributions. Communications in Statistics - Theory and Methods, 44, (19), 4096-4113.
Bashir, S., Rasul, M., (2015). Some properties of the weighted Lindley distribution. EPRA Internation Journal of Economic and Business Review, 3, (8), 11-17.
Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K. and Husain, H. A., (2011). A two-parameter weighted Lindley distribution and its applications to survival data. Mathematics and Computers in Simulation, 81, (6), 1190-1201.
Mazucheli, J., Louzada, F., Ghitany, M. E., (2013). Comparison of estimation methods for the parameters of the weighted Lindley distribution. Applied Mathematics and Computation, 220, 463-471.
Mazucheli, J., Coelho-Barros, E. A. and Achcar, J. (2016). An alternative reparametrization on the weighted Lindley distribution. Pesquisa Operacional, (to appear).
1 2 3 4 5 6 7 8 9 10 11 | set.seed(1)
x <- rdwlindley(n = 1000, theta = 1.5, alpha = 1.5)
plot(table(x) / sum(table(x)))
points(unique(x),ddwlindley(unique(x), theta = 1.5, alpha = 1.5))
## fires in Greece data (from Bakouch et al., 2014)
data(fires)
library(fitdistrplus)
fit <- fitdist(fires, 'dwlindley', start = list(theta = 0.30, alpha = 1.0), discrete = TRUE)
gofstat(fit, discrete = TRUE)
plot(fit)
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