flexCountReg (version 0.1.1)

PoissonLindleyLognormal: Poisson-Lindley-Lognormal Distribution

Description

These functions provide density, distribution, quantile, and random generation for the Poisson-Lindley-Lognormal (PLL) Distribution.

Usage

dplindLnorm(
  x,
  mean = 1,
  theta = 1,
  sigma = 1,
  ndraws = 1500,
  log = FALSE,
  hdraws = NULL
)
pplindLnorm(
  q,
  mean = 1,
  theta = 1,
  lambda = NULL,
  sigma = 1,
  ndraws = 1500,
  lower.tail = TRUE,
  log.p = FALSE
)
qplindLnorm(p, mean = 1, theta = 1, sigma = 1, ndraws = 1500, lambda = NULL)
rplindLnorm(n, mean = 1, theta = 1, sigma = 1, ndraws = 1500, lambda = NULL)

Value

dplindLnorm gives the density, pplindLnorm gives the distribution function, qplindLnorm gives the quantile function, and rplindLnorm generates random deviates.

The length of the result is determined by n for rplindLnorm, and is the maximum of the lengths of the numerical arguments for the other functions.

Arguments

x

numeric value or vector of values.

mean

mean (>0).

theta

Poisson-Lindley theta parameter (>0).

sigma

lognormal sigma parameter (>0).

ndraws

number of Halton draws.

log

return log-density.

hdraws

optional Halton draws.

q

quantile or vector of quantiles.

lambda

optional lambda parameter (>0).

lower.tail

TRUE returns P[X $$\leq$$ x].

log.p

return log-CDF.

p

probability or vector of probabilities.

n

number of random draws.

Details

The PLL is a 3-parameter count distribution that captures high mass at small y and allows flexible heavy tails.

dplind computes the PLL density. pplind computes the PLL CDF. qplind computes quantiles. rplind generates random draws.

The PMF is: $$ f(y|\mu,\theta,\sigma)=\int_0^\infty \frac{\theta^2\mu^y x^y(\theta+\mu x+y+1)} {(\theta+1)(\theta+\mu x)^{y+2}} \frac{\exp\left(-\frac{\ln^2(x)}{2\sigma^2}\right)} {x\sigma\sqrt{2\pi}}dx $$

Mean: $$ E[y]=\mu=\frac{\lambda(\theta+2)e^{\sigma^2/2}} {\theta(\theta+1)} $$

Halton draws are used to evaluate the integral.

Examples

dplindLnorm(0, mean=0.75, theta=7, sigma=2, ndraws=10)
pplindLnorm(0:10, mean=0.75, theta=7, sigma=2, ndraws=10)
qplindLnorm(c(0.1,0.5,0.9), lambda=4.67, theta=7, sigma=2)
rplindLnorm(5, mean=0.75, theta=7, sigma=2)