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 new weighted Lindley distribution with parameters theta and alpha.
1 2 3 4 5 6 7 8 9 10 | dnwlindley(x, theta, alpha, log = FALSE)
pnwlindley(q, theta, alpha, lower.tail = TRUE, log.p = FALSE)
qnwlindley(p, theta, alpha, lower.tail = TRUE, log.p = FALSE, L = 1e-04,
U = 50)
rnwlindley(n, theta, alpha, L = 1e-04, U = 50)
hnwlindley(x, theta, alpha, log = FALSE)
|
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. |
L, U |
interval which |
n |
number of observations. If |
Probability density function
f(x\mid θ,α )={\frac{{θ }^{2}≤ft( 1+α \right) ^{2}}{α ≤ft( α θ +α +θ +2\right) }}≤ft( 1+x\right) ≤ft( 1-e{^{-θ α x}}\right) e{^{-θ x}}
Cumulative distribution function
F(x\mid θ,α )=1-{\frac{≤ft( 1+α \right) ^{2}≤ft( θ x+θ +1\right) e{^{-θ x}}}{α ≤ft( α θ +α +θ +2\right) }}+{\frac{≤ft( θ α x+α θ +θ x+θ +1\right) e{^{-θ x}}e{^{-θ α x}}}{α ≤ft(α θ +α +θ +2\right) }}
Quantile function
\code{does not have a closed mathematical expression}
Hazard rate function
h(x\mid θ,α )=\frac{{θ }^{2}≤ft( 1+α \right) ^{2}≤ft( 1+x\right) ≤ft( 1-e{^{-θ α x}}\right) e{^{-θ x}}}{≤ft( 1+α \right) ^{2}≤ft( θ x+θ +1\right) e{^{-θ x}-}≤ft( θ α x+α θ +θ x+θ +1\right) e{^{-θ x}}e{^{-θ α x}}}
dnwlindley
gives the density, pnwlindley
gives the distribution function, qnwlindley
gives the quantile function, rnwlindley
generates random deviates and hnwlindley
gives the hazard rate function.
Invalid arguments will return an error message.
The uniroot
function with default arguments is used to find out the quantiles.
Josmar Mazucheli jmazucheli@gmail.com
Larissa B. Fernandes lbf.estatistica@gmail.com
[d-h-p-q-r]nwlindley are calculated directly from the definitions. rnwlindley
uses the quantile function.
Asgharzadeh, A., Bakouch, H. S., Nadarajah, S., Sharafi, F., (2016). A new weighted Lindley distribution with application. Brazilian Journal of Probability and Statistics, 30, 1-27.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | set.seed(1)
x <- rnwlindley(n = 1000, theta = 1.5, alpha = 1.5)
R <- range(x)
S <- seq(from = R[1], to = R[2], by = 0.1)
plot(S, dnwlindley(S, theta = 1.5, alpha = 1.5), 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)
pnwlindley(q, theta = 1.5, alpha = 1.5, lower.tail = TRUE)
pnwlindley(q, theta = 1.5, alpha = 1.5, lower.tail = FALSE)
qnwlindley(p, theta = 1.5, alpha = 1.5, lower.tail = TRUE)
qnwlindley(p, theta = 1.5, alpha = 1.5, lower.tail = FALSE)
library(fitdistrplus)
fit <- fitdist(x, 'nwlindley', start = list(theta = 1.5, alpha = 1.5))
plot(fit)
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