The Tobit Distribution
Density, distribution function, quantile function and random generation for the Tobit model.
dtobit(x, mean = 0, sd = 1, Lower = 0, Upper = Inf, log = FALSE)
ptobit(q, mean = 0, sd = 1, Lower = 0, Upper = Inf,
lower.tail = TRUE, log.p = FALSE)
qtobit(p, mean = 0, sd = 1, Lower = 0, Upper = Inf,
lower.tail = TRUE, log.p = FALSE)
rtobit(n, mean = 0, sd = 1, Lower = 0, Upper = Inf)x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
If |
Lower, Upper |
vector of lower and upper thresholds. |
mean, sd, lower.tail, log, log.p |
see |
See tobit, the VGAM family function
for estimating the parameters,
for details.
Note that the density at Lower and Upper is the
the area to the left and right of those points.
Thus there are two spikes (but less in value); see the example below.
Consequently, dtobit(Lower) + dtobit(Upper) + the area
in between equals unity.
dtobit gives the density,
ptobit gives the distribution function,
qtobit gives the quantile function, and
rtobit generates random deviates.
T. W. Yee
mu <- 0.5; x <- seq(-2, 4, by = 0.01)
Lower <- -1; Upper <- 2.0
integrate(dtobit, lower = Lower, upper = Upper,
mean = mu, Lower = Lower, Upper = Upper)$value +
dtobit(Lower, mean = mu, Lower = Lower, Upper = Upper) +
dtobit(Upper, mean = mu, Lower = Lower, Upper = Upper) # Adds to unity
## Not run:
plot(x, ptobit(x, m = mu, Lower = Lower, Upper = Upper),
type = "l", ylim = 0:1, las = 1, col = "orange",
ylab = paste("ptobit(m = ", mu, ", sd = 1, Lower =", Lower,
", Upper =", Upper, ")"),
main = "Orange is cumulative distribution function; blue is density",
sub = "Purple lines are the 10,20,...,90 percentiles")
abline(h = 0)
lines(x, dtobit(x, m = mu, Lower = Lower, Upper = Upper), col = "blue")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qtobit(probs, m = mu, Lower = Lower, Upper = Upper)
lines(Q, ptobit(Q, m = mu, Lower = Lower, Upper = Upper),
col = "purple", lty = "dashed", type = "h")
lines(Q, dtobit(Q, m = mu, Lower = Lower, Upper = Upper),
col = "darkgreen", lty = "dashed", type = "h")
abline(h = probs, col = "purple", lty = "dashed")
max(abs(ptobit(Q, m = mu, Lower = Lower, Upper = Upper) - probs)) # Should be 0
endpts <- c(Lower, Upper) # Endpoints have a spike (not quite, actually)
lines(endpts, dtobit(endpts, m = mu, Lower = Lower, Upper = Upper),
col = "blue", lwd = 3, type = "h")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.