lientz: The empirical Lientz function and the Lientz mode estimator

Description Usage Arguments Details Value Note References See Also Examples

View source: R/lientz.R

Description

The Lientz mode estimator is nothing but the value minimizing the empirical Lientz function. A 'plot' and a 'print' methods are provided.

Usage

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lientz(x, bw = NULL)

## S3 method for class 'lientz'
plot(x, zoom = FALSE, ...)

## S3 method for class 'lientz'
print(x, digits = NULL, ...)

## S3 method for class 'lientz'
mlv(x, bw = NULL, abc = FALSE, par = shorth(x), optim.method = "BFGS", ...)

Arguments

x

numeric (vector of observations) or an object of class "lientz".

bw

numeric. The smoothing bandwidth to be used. Should belong to (0, 1). Parameter 'beta' in Lientz (1970) function.

zoom

logical. If TRUE, one can zoom on the graph created.

...

if abc = FALSE, further arguments to be passed to optim, or further arguments to be passed to plot.

digits

numeric. Number of digits to be printed.

abc

logical. If FALSE (the default), the Lientz empirical function is minimised using optim.

par

numeric. The initial value used in optim.

optim.method

character. If abc = FALSE, the method used in optim.

Details

The Lientz function is the smallest non-negative quantity S(x,b), where b = bw, such that

F(x+S(x,b)) - F(x-S(x,b)) >= b.

Lientz (1970) provided a way to estimate S(x,b); this estimate is what we call the empirical Lientz function.

Value

lientz returns an object of class c("lientz", "function"); this is a function with additional attributes:

mlv.lientz returns a numeric value, the mode estimate. If abc = TRUE, the x value minimizing the Lientz empirical function is returned. Otherwise, the optim method is used to perform minimization, and the attributes: 'value', 'counts', 'convergence' and 'message', coming from the optim method, are added to the result.

Note

The user may call mlv.lientz through mlv(x, method = "lientz", ...).

References

See Also

mlv for general mode estimation; shorth for the shorth estimate of the mode

Examples

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# Unimodal distribution
x <- rbeta(1000,23,4)

## True mode
betaMode(23, 4)

## Lientz object
f <- lientz(x, 0.2)
print(f)
plot(f)

## Estimate of the mode
mlv(f)              # optim(shorth(x), fn = f)
mlv(f, abc = TRUE)  # x[which.min(f(x))]
mlv(x, method = "lientz", bw = 0.2)

# Bimodal distribution
x <- c(rnorm(1000,5,1), rnorm(1500, 22, 3))
f <- lientz(x, 0.1)
plot(f)

modeest documentation built on Nov. 18, 2019, 5:07 p.m.