ShiftGomp {extraDistr} | R Documentation |
Shifted Gompertz distribution
Description
Density, distribution function, and random generation for the shifted Gompertz distribution.
Usage
dsgomp(x, b, eta, log = FALSE)
psgomp(q, b, eta, lower.tail = TRUE, log.p = FALSE)
rsgomp(n, b, eta)
Arguments
x , q |
vector of quantiles. |
b , eta |
positive valued scale and shape parameters; both need to be positive. |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
n |
number of observations. If |
Details
If follows exponential distribution parametrized by scale
and
follows reparametrized Gumbel distribution with cumulative distribution function
parametrized by
scale
and shape
, then
follows shifted
Gompertz distribution parametrized by scale
and shape
.
The above relation is used by
rsgomp
function for random generation from
shifted Gompertz distribution.
Probability density function
Cumulative distribution function
References
Bemmaor, A.C. (1994). Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity. [In:] G. Laurent, G.L. Lilien & B. Pras. Research Traditions in Marketing. Boston: Kluwer Academic Publishers. pp. 201-223.
Jimenez, T.F. and Jodra, P. (2009). A Note on the Moments and Computer Generation of the Shifted Gompertz Distribution. Communications in Statistics - Theory and Methods, 38(1), 78-89.
Jimenez T.F. (2014). Estimation of the Parameters of the Shifted Gompertz Distribution, Using Least Squares, Maximum Likelihood and Moments Methods. Journal of Computational and Applied Mathematics, 255(1), 867-877.
Examples
x <- rsgomp(1e5, 0.4, 1)
hist(x, 50, freq = FALSE)
curve(dsgomp(x, 0.4, 1), 0, 30, col = "red", add = TRUE)
hist(psgomp(x, 0.4, 1))
plot(ecdf(x))
curve(psgomp(x, 0.4, 1), 0, 30, col = "red", lwd = 2, add = TRUE)