| Type: | Package |
| Title: | Three-Parameter Generalized Lindley-Poisson Distribution Functions |
| Version: | 0.1.0 |
| Description: | Provides functions for random generation, density, cumulative distribution, quantile function, moments, and log-likelihood for a three-parameter generalized Lindley-Poisson mixture model. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | stats |
| NeedsCompilation: | no |
| Packaged: | 2026-05-29 01:51:18 UTC; nisan |
| Author: | Nisansala Wijerathna [aut, cre], DiangLiang Deng [ths] |
| Maintainer: | Nisansala Wijerathna <nisansaladulmini32@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2026-06-02 07:50:08 UTC |
Density Function of the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Computes the probability mass function of the Three-Parameter Generalized Lindley-Poisson distribution.
Usage
dtpglp(y, pi, theta1, theta2, log = FALSE)
Arguments
y |
Numeric vector of non-negative integers. |
pi |
Numeric. Mixing probability in [0,1]. |
theta1 |
Numeric. Positive parameter. |
theta2 |
Numeric. Positive parameter. |
log |
Logical. If TRUE, returns log-probabilities. |
Value
Numeric vector of probabilities.
Examples
dtpglp(0:5, pi = 0.6, theta1 = 1, theta2 = 2)
Log-Likelihood Function for the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Computes the log-likelihood.
Usage
logLik_tpglp(y, pi, theta1, theta2)
Arguments
y |
Numeric vector of counts. |
pi |
Numeric. Mixing probability. |
theta1 |
Numeric. Positive parameter. |
theta2 |
Numeric. Positive parameter. |
Value
Numeric value.
Examples
y <- rpois(100, 2)
logLik_tpglp(y, pi = 0.5, theta1 = 1, theta2 = 2)
Mean of the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Computes the mean.
Usage
mean_tpglp(pi, theta1, theta2)
Arguments
pi |
Numeric. Mixing probability. |
theta1 |
Numeric. Positive parameter. |
theta2 |
Numeric. Positive parameter. |
Value
Numeric value.
Examples
mean_tpglp(pi = 0.6, theta1 = 1, theta2 = 2)
Distribution Function of the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Computes cumulative probabilities.
Usage
ptpglp(q, pi, theta1, theta2, lower.tail = TRUE)
Arguments
q |
Numeric vector of quantiles. |
pi |
Numeric. Mixing probability in [0,1]. |
theta1 |
Numeric. Positive parameter. |
theta2 |
Numeric. Positive parameter. |
lower.tail |
Logical. |
Value
Numeric vector of probabilities.
Examples
ptpglp(5, pi = 0.6, theta1 = 1, theta2 = 2)
Quantile Function of the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Computes quantiles numerically via inversion.
Usage
qtpglp(p, pi, theta1, theta2, max_y = 1000, lower.tail = TRUE)
Arguments
p |
Numeric vector of probabilities. |
pi |
Numeric. Mixing probability. |
theta1 |
Numeric. Positive parameter. |
theta2 |
Numeric. Positive parameter. |
max_y |
Integer search limit. |
lower.tail |
Logical. |
Value
Numeric vector of quantiles.
Examples
qtpglp(0.5, pi = 0.6, theta1 = 1, theta2 = 2)
Random Generation from the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Generates random observations from a two-component mixture model: an Exponential-Poisson (geometric) component and a Gamma-Poisson (negative binomial) component.
Usage
rtpglp(n, pi, theta1, theta2, seed = NULL)
Arguments
n |
number of observations |
pi |
mixing probability |
theta1 |
positive parameter |
theta2 |
positive parameter |
seed |
optional seed |
Details
For each observation:
With probability
\pi:\lambda \sim Exp(1/\theta_1)With probability
1-\pi:\lambda \sim Gamma(shape=2, rate=1/\theta_2)Then:
Y \sim Poisson(\lambda)
Value
vector of counts
Examples
rtpglp(100, pi = 0.6, theta1 = 1, theta2 = 2)
rtpglp(100, pi = 0.6, theta1 = 1, theta2 = 2, seed = 123)
Variance of the Three-Parameter Generalized Lindley-Poisson Distribution
Description
Computes the variance.
Usage
var_tpglp(pi, theta1, theta2)
Arguments
pi |
Numeric. Mixing probability. |
theta1 |
Numeric. Positive parameter. |
theta2 |
Numeric. Positive parameter. |
Value
Numeric value.
Examples
var_tpglp(pi = 0.6, theta1 = 1, theta2 = 2)