fts {tpn}

Flexible truncated positive normal

Description

Density, distribution function and random generation for the flexible truncated positive (ftp) class discussed in Gomez et al. (2022).

Usage

dfts(x, sigma, lambda, dist="norm", log = FALSE)
pfts(x, sigma, lambda, dist="norm", lower.tail=TRUE, log.p=FALSE)
qfts(p, sigma, lambda, dist="norm")
rfts(n, sigma, lambda, dist="norm")

Arguments

x

vector of quantiles

p

vector of probabilities

n

number of observations

sigma

scale parameter for the distribution

lambda

shape parameter for the distribution

dist

standard symmetrical distribution. Avaliable options: norm (default), logis, cauchy and laplace.

log, log.p

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

dfts gives the density, pfts gives the distribution function, qfts gives the quantile function and rfts generates random deviates.

The length of the result is determined by n for rbtpn, 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 have fts distribution with parameters \sigma>0 and \lambda \in R if its probability density function can be written as

f(y; \sigma, \lambda, q) = \frac{g_0(\frac{y}{\sigma}-\lambda)}{\sigma G_0(\lambda)}, y>0,

where g_0(\cdot) and G_0(\cdot) denote the pdf and cdf for the specified distribution. The case where g_0(\cdot) and G_0(\cdot) are from the standard normal model is known as the truncated positive normal model discussed in Gomez et al. (2018).

Author(s)

Gallardo, D.I., Gomez, H.J. and Gomez, Y.M.

References

Gomez, H.J., Gomez, H.W., Santoro, K.I., Venegas, O., Gallardo, D.I. (2022). A Family of Truncation Positive Distributions. Submitted.

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

dfts(c(1,2), sigma=1, lambda=1, dist="logis")
pfts(c(1,2), sigma=1, lambda=1, dist="logis")
rfts(n=10, sigma=1, lambda=1, dist="logis")