fts: Flexible truncated positive normal

In tpn: Truncated Positive Normal Model and Extensions

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")

tpn documentation built on Sept. 28, 2023, 1:06 a.m.