utpn {tpn}

Truncated positive normal

Description

Density, distribution function and random generation for the unit truncated positive normal (utpn) type 1 or 2 discussed in Gomez, Gallardo and Santoro (2021).

Usage

dutpn(x, sigma = 1, lambda = 0, type = 1, log = FALSE)
putpn(x, sigma = 1, lambda = 0, type = 1, lower.tail = TRUE, log = FALSE)
qutpn(p, sigma = 1, lambda = 0, type = 1)
rutpn(n, sigma = 1, lambda = 0, type = 1)

Arguments

x

vector of quantiles

n

number of observations

p

vector of probabilities

sigma

scale parameter for the distribution

lambda

shape parameter for the distribution

type

to distinguish the type of the utpn model: 1 (default) or 2.

log

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].

Details

Random generation is based on the inverse transformation method.

Value

dutpn gives the density, putpn gives the distribution function, qutpn provides the quantile function and rutpn generates random deviates.

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

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

A variable has utpn distribution with scale parameter \sigma>0 and shape parameter \lambda \in R if its probability density function can be written as

f(y; \sigma, \lambda) = \frac{\phi\left(\frac{1-y}{\sigma y}-\lambda\right)}{\sigma y^2\Phi(\lambda)}, y>0, \mbox{(type 1),}

f(y; \sigma, \lambda) = \frac{\phi\left(\frac{y}{\sigma (1-y)}-\lambda\right)}{\sigma (1-y)^2\Phi(\lambda)}, y>0, \mbox{(type 2),}

f(y; \sigma, \lambda) = \frac{\phi\left(\frac{\log(y)}{\sigma}+\lambda\right)}{\sigma y\Phi(\lambda)}, y>0, \mbox{(type 3),}

f(y; \sigma, \lambda) = \frac{\phi\left(\frac{\log(1-y)}{\sigma}+\lambda\right)}{\sigma (1-y)\Phi(\lambda)}, y>0, \mbox{(type 4),}

where \phi(\cdot) and \Phi(\cdot) denote the density and cumulative distribution functions for the standard normal distribution.

Author(s)

Gallardo, D.I.

References

Gomez, H.J., Olmos, N.M., Varela, H., Bolfarine, H. (2018). Inference for a truncated positive normal distribution. Applied Mathemetical Journal of Chinese Universities, 33, 163-176.

Examples

dutpn(c(0.1,0.2), sigma=1, lambda=-1)
putpn(c(0.1,0.2), sigma=1, lambda=-1)
rutpn(n=10, sigma=1, lambda=-1)