Maximum likelihood estimated distribution

Density, distribution function, quantile function and random generation for a univariate distribution estimated by maximum likelihood.

dml(x, obj, log = FALSE)

pml(q = q, obj, lower.tail = TRUE, log.p = FALSE)

qml(p = p, obj, lower.tail = TRUE, log.p = FALSE)

rml(n = n, obj)

Arguments

x, q	vector of quantiles.
obj	an univariateML object.
log, log.p	logical; if TRUE, the probabilities p are gives as log(p).
lower.tail	logical; if TRUE (default), the probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\)
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Value

dml gives the density, pml gives the distribution function, qml gives the quantile function, and rml generates random deviates.

Details

dml is the density, pml is the distribution function, qml is the quantile function, and rml is the random variable generator.

These functions work like their counterparts in `stats`, e.g. Normal. The univariateML object contains both maximum likelihood estimates and the identity of the model these estimates were calculated under. These functions are wrappers around underlying density, distribution, quantile and random generation functions where unknown parameters are filled with the maximum likelihood estimates. See the example.

Examples

## Simple example
obj <- mlnorm(airquality$Wind)
dml(0.5, obj) == dnorm(0.5, mean = obj[1], sd = obj[2])
#> [1] TRUE

## We study the Beta prime model applied to the airquality data set.
obj <- mlbetapr(airquality$Wind)

## Example copied from 'stats::dnorm'.
par(mfrow = c(2, 1))
plot(function(x) dml(x, obj, log = TRUE),
  from = 0, to = 20,
  main = "Logarithm of Density", ylab = NA, lwd = 2
)
curve(log(dml(x, obj)), add = TRUE, col = "red", lwd = 2, lty = 2)
mtext("dml(x, obj, log = TRUE)", adj = 0)
mtext("log(dml(x, obj))", col = "red", adj = 1)

plot(function(x) pml(x, obj, log = TRUE),
  from = 0, to = 20,
  main = "Logarithm of Cumulative Probability", ylab = NA, lwd = 2
)
curve(log(pml(x, obj)), add = TRUE, col = "red", lwd = 2, lty = 2)
mtext("pml(x, obj, log = TRUE)", adj = 0)
mtext("log(pml(x, obj))", col = "red", adj = 1)