Package 'tpglp'

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)

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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)

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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)

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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)

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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)

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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)

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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)

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