Package 'ztpln'

The zero-truncated compund poisson-lognormal distributions

Description

Density function and random generation for Zero-Trauncated Poisson Lognormal distribution with parameters mu and sd sig.

Usage

dztpln(x, mu, sig, log = FALSE, type1 = TRUE)

rztpln(n, mu, sig, type1 = TRUE)

Arguments

x	vector of (non-negative integer) quantiles.
mu	mean of lognormal distribution.
sig	standard deviation of lognormal distribution.
log	logical; if TRUE, probabilities p are given as log(p).
type1	logical; if TRUE, Use type 1 ztpln else use type 2.
n	number of random values to return.

Details

A compound Poisson-lognormal distribution is a Poisson probability distribution where its parameter $\lambda$ is a random variable with lognormal distribution, that is to say $log\lambda$ are normally distributed with mean $\mu$ and variance $\sigma^2$ (Bulmer 1974). The zero-truncated Poisson-lognormal distribution can be derived from a zero-truncated Poisson distribution.

Type 1 ZTPLN truncates zero based on Poisson-lognormal distribution and type 2 ZTPLN truncates zero based on zero-truncated Poisson distribution. For mathematical details, please see vignette("ztpln")

Value

dztpln gives the (log) density and rztpln generates random variates.

References

Bulmer, M. G. 1974. On Fitting the Poisson Lognormal Distribution to Species-Abundance Data. Biometrics 30:101-110.

See Also

dztplnm

Examples

rztpln(n = 10, mu = 0, sig = 1, type1 = TRUE)
rztpln(n = 10, mu = 6, sig = 4, type1 = TRUE)
dztpln(x = 1:5, mu = 1, sig = 2)

---

The zero-truncated compund poisson-lognormal distributions mixture

Description

Density function and random generation for Zero-Truncated Poisson Lognormal distribution with parameters mu, sig, and theta.

Usage

dztplnm(x, mu, sig, theta, log = FALSE, type1 = TRUE)

rztplnm(n, mu, sig, theta, type1 = TRUE)

Arguments

x	vector of (non-negative integer) quantiles.
mu	vector of mean of lognormal distribution in sample.
sig	vector standard deviation of lognormal distribution in sample.
theta	vector of mixture weights
log	logical; if TRUE, probabilities p are given as log(p).
type1	logical; if TRUE, Use type 1 ztpln else use type 2.
n	number of random values to return.

Details

Type 1 ZTPLN truncates zero based on Poisson-lognormal distribution and type 2 ZTPLN truncates zero based on zero-truncated Poisson distribution. For mathematical details, please see vignette("ztpln")

Value

dztplnm gives the (log) density and rztplnm generates random variates. function, qpois gives the quantile function, and rpois generates random deviates.

See Also

dztpln

Examples

rztplnm(n = 100, mu = c(0, 5), sig = c(1, 2), theta = c(0.2, 0.8))
dztplnm(x = 1:100, mu = c(0, 5), sig = c(1, 2), theta = c(0.2, 0.8))
dztplnm(x = 1:100, mu = c(0, 5), sig = c(1, 2), theta = c(0.2, 0.8), type1 = FALSE)

---

MLE for the Zero-truncated Poisson Lognormal distribution

Description

ztplnMLE fits the Zero-truncated Poisson lognormal distribution to data and estimates parameters mean mu and standard deviation sig in the lognormal distribution

Usage

ztplnMLE(
  n,
  lower_mu = 0,
  upper_mu = log(max(n)),
  lower_sig = 0.001,
  upper_sig = 10,
  type1 = TRUE
)

Arguments

n	a integer vector of counts
lower_mu, upper_mu	numeric values of lower and upper bounds for mean of the variables's natrual logarithm.
lower_sig, upper_sig	numeric values of lower and upper bounds for standard deviatoin of the variables's natrual logarithm
type1	logical; if TRUE, Use type 1 ztpln else use type 2.

Details

The function searches the maximum likelihood estimates of mean mu and standard deviation sig using the optimization procedures in nlminb.

Value

convergence	An integer code. 0 indicates successful convergence.
iterations	Number of iterations performed.
message	A character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation.
evaluation	Number of objective function and gradient function evaluations
mu	Maximum likelihood estimates of mu
sig	Maximum likelihood estimates of sig
loglik	loglikelihood

Examples

y <- rztpln(100, 3, 2)
ztplnMLE(y)

---

MLE for the Zero-truncated Poisson Lognormal mixture distribtuion

Description

ztplnmMLE fits the Zero-truncated Poisson lognormal mixture distribution to data and estimates parameters mean mu, standard deviation sig and mixture weight theta in the lognormal distribution.

Usage

ztplnmMLE(
  n,
  K = 2,
  lower_mu = rep(0, K),
  upper_mu = rep(log(max(n)), K),
  lower_sig = rep(0.001, K),
  upper_sig = rep(10, K),
  lower_theta = rep(0.001, K),
  upper_theta = rep(0.999, K),
  type1 = TRUE,
  message = FALSE
)

Arguments

n	a vector of counts
K	number of components
lower_mu, upper_mu	numeric values of lower and upper bounds for mean of the variables's natural logarithm.
lower_sig, upper_sig	numeric values of lower and upper bounds for standard deviation of the variables's natural logarithm
lower_theta, upper_theta	numeric values of lower and upper bounds for mixture weights.
type1	logical; if TRUE, Use type 1 ztpln else use type 2.
message	mean of lognormal distribution in sample 3.

Details

The function searches the maximum likelihood estimators of mean vector mu, standard deviation vector sig and mixture weight vector theta using the optimization procedures in nlminb.

Value

convergence	An integer code. 0 indicates successful convergence.
iterations	Number of iterations performed.
message	A character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation.
evaluation	Number of objective function and gradient function evaluations
mu	Maximum likelihood estimates of mu
sig	Maximum likelihood estimates of sig
theta	Maximum likelihood estimates of theta
loglik	loglikelihood

Examples

y <- rztplnm(100, c(1, 10), c(2, 1), c(0.2, 0.8))
ztplnmMLE(y)

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