The Truncated Student-t Distribution
Density, distribution function, quantile function, and random generation
for the left and/or right truncated student-t distribution with df
degrees of freedom.
dtt(x, location = 0, scale = 1, df, left = -Inf, right = Inf, log = FALSE) ptt(q, location = 0, scale = 1, df, left = -Inf, right = Inf, lower.tail = TRUE, log.p = FALSE) rtt(n, location = 0, scale = 1, df, left = -Inf, right = Inf) qtt(p, location = 0, scale = 1, df, left = -Inf, right = Inf, lower.tail = TRUE, log.p = FALSE)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
location |
location parameter. |
scale |
scale parameter. |
df |
degrees of freedom (> 0, maybe non-integer). |
left |
left censoring point. |
right |
right censoring point. |
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]. |
If location or scale are not specified they assume the default values
of 0 and 1, respectively. left and right have the defaults -Inf and Inf respectively.
The truncated student-t distribution has density
f(x) = 1/σ τ((x - μ)/σ) / (T((right - μ)/σ) - T((left - μ)/σ))
for left ≤ x ≤ right, and 0 otherwise.
where T and τ are the cumulative distribution function
and probability density function of the student-t distribution with
df degrees of freedom respectively, μ is the location of the
distribution, and σ the scale.
dtt gives the density, ptt gives the distribution
function, qtt gives the quantile function, and rtt
generates random deviates.
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