DPLindley: Discrete Power Lindley Distribution

In LindleyR: The Lindley Distribution and Its Modifications

Description

Probability mass function, distribution function, quantile function and random number generation for the discrete power Lindley distribution with parameters theta and alpha.

Usage

ddplindley(x, theta, alpha, log = FALSE)

pdplindley(q, theta, alpha, lower.tail = TRUE, log.p = FALSE)

qdplindley(p, theta, alpha, lower.tail = TRUE, log.p = FALSE)

rdplindley(n, theta, alpha)

Arguments

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 length(n) > 1, the length is taken to be the number required.

Details

Probability mass function

P(X=x\mid θ ,α )=∑\limits_{i=0}^{1}≤ft( -1\right) ^{i}≤ft( 1+{\frac{θ }{θ +1}}≤ft( x+i\right) ^{α }\right) \ e^{-θ ≤ft( x+i\right) ^{α}}

Particular case: α = 1 the one-parameter discrete Lindley distribution.

Value

ddplindley gives the probability mass function, pdplindley gives the distribution function, qdplindley gives the quantile function and rdplindley generates random deviates.

Invalid arguments will return an error message.

Author(s)

Josmar Mazucheli [e-mail]

Ricardo P. de Oliveira [e-mail]

Source

[d-p-q-r]dplindley are calculated directly from the definitions. rdplindley uses the discretize values.

References

Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N. and Al-Enezi, L. J., (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64, 20-33.

Mazucheli, J., Ghitany, M. E. and Louzada, F., (2013). Power Lindley distribution: Diferent methods of estimation and their applications to survival times data. Journal of Applied Statistical Science, 21, (2), 135-144.

See Also

PLindley.

Examples

set.seed(1)
x <- rdplindley(n = 1000, theta = 1.5, alpha = 0.5)
plot(table(x) / sum(table(x)))
points(unique(x),ddplindley(unique(x), theta = 1.5, alpha = 0.5))

## fires in Greece data (from Bakouch et al., 2014)
data(fires)
library(fitdistrplus)
fit <- fitdist(fires, 'dplindley', start = list(theta = 0.30, alpha = 1.0), discrete = TRUE)
gofstat(fit, discrete = TRUE)
plot(fit)

LindleyR documentation built on May 1, 2019, 8:05 p.m.