Discrete Weighted Lindley Distribution

Description

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

Usage

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)

Arguments

Details

Probability mass function

P(X=xmid θ ,α )=frac{1}{≤ft( θ +α ight) Γ ≤ft( α ight) }∑limits_{i=0}^{1}≤ft( -1 ight) ^{i}≤ft{ ≤ft( θ +α ight) Γ ≤ft[ α ,θ ≤ft( x+i ight) ight] +≤ft[θ ≤ft( x+i ight) ight] ^{α }e^{-θ ≤ft( x+i ight)} ight}

where Γ ≤ft(α,θ x ight) = 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.

Value

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.

Author(s)

Josmar Mazucheli jmazucheli@gmail.com

Ricardo P. de Oliveira rpuziol.oliveira@gmail.com

Source

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

References

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).

See Also

WLindley.

Examples

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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LindleyR)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LindleyR/DWLindley.Rd_%03d_medium.png", width=480, height=480)
> ### Name: DWLindley
> ### Title: Discrete Weighted Lindley Distribution
> ### Aliases: DWLindley ddwlindley pdwlindley qdwlindley rdwlindley
> 
> ### ** Examples
> 
> 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)
Loading required package: MASS
> fit <- fitdist(fires, 'dwlindley', start = list(theta = 0.30, alpha = 1.0), discrete = TRUE)
> gofstat(fit, discrete = TRUE)
Chi-squared statistic:  6.904896 
Degree of freedom of the Chi-squared distribution:  6 
Chi-squared p-value:  0.329732 
Chi-squared table:
      obscounts theocounts
<= 0  16.000000  15.539159
<= 1  13.000000  14.025216
<= 2  14.000000  13.367709
<= 4  20.000000  23.144651
<= 5  13.000000   9.501967
<= 7  12.000000  15.078807
<= 9  15.000000  10.670369
<= 12 13.000000  10.063927
> 12   7.000000  11.608194

Goodness-of-fit criteria
                               1-mle-dwlindley
Aikake's Information Criterion        682.7097
Bayesian Information Criterion        688.3340
> plot(fit)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>