Description Usage Arguments Details Value Author(s) References See Also Examples
Density, distribution function, quantile function, random number
generation for the BMT-Phi distribution with mean equal to
standard deviation equal to
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vector of quantiles.
vector of means.
vector of standard deviations.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].
vector of probabilities.
number of observations. If
sd are not specified they assume the
default values of 0 and 1, respectively.
The BMT-Phi distribution is the BMT distribution with κ_l = κ_r = 0.58029164978583758. The BMT-Phi cumulative distribution function (cdf) is the closest BMT cdf to the normal cdf with the same mean and standard deviation.
dBMT.Phi gives the density,
pBMT.Phi the distribution
qBMT.Phi the quantile function, and
generates random deviates.
The length of the result is determined by
is the maximum of the lengths of the numerical arguments for the other
The numerical arguments other than
n are recycled to the length of
the result. Only the first elements of the logical arguments are used.
sd <= 0 is an error and returns
Camilo Jose Torres-Jimenez [aut,cre] email@example.com
Torres-Jimenez, C. J. (2018), The BMT Item Response Theory model: A new skewed distribution family with bounded domain and an IRT model based on it, PhD thesis, Doctorado en ciencias - Estadistica, Universidad Nacional de Colombia, Sede Bogota.
Distributions for other standard distributions.
pBMT for the BMT distribution and
the BMT-Psi distribution.
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layout(matrix(1:4,2,2)) curve(pnorm(x), -4, 4, col = "red", lty = 2, ylab = "cdf") curve(pBMT.Phi(x), add = TRUE, col = "blue", lty = 3) legend("topleft", legend = c("norm(0,1)","BMT-Phi(0,1)"), bty = "n", col = c("red","blue"), lty = 2:3) curve(pnorm(x)-pBMT.Phi(x), -4, 4) curve(qnorm(x), col = "red", lty = 2, xlab = "p", ylab = "qf") curve(qBMT.Phi(x), add = TRUE, col = "blue", lty = 3) hist(rBMT.Phi(10000), freq = FALSE, breaks = seq(-4,4,0.25), border = "blue") curve(dnorm(x), add = TRUE, col = "red", lty = 2) curve(dBMT.Phi(x), add = TRUE, col = "blue", lty = 3)
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