Determining High Density Region for a distribution in R

问题

Background:

Normally, R gives quantiles for well-known distributions. Out of these quantiles, the lower 2.5% up to the upper 97.5% covers 95% of the area under these distributions.

Question:

Suppose I have a F distribution (df1 = 10, df2 = 90). In R, how can I determine the 95% of the area under this distribution such that this 95% only covers the HIGH DENSITY area, not the 95% that R normally gives (see my R code Below)?

Note: Clearly, the highest density is the "mode" (dashed line in the pic below). So I guess, one must move from "mode" toward the tails.

Here is my R code:

curve(df(x, 10, 90), 0, 3, ylab = 'Density', xlab = 'F value', lwd = 3)

Mode = ( (10 - 2) / 10 ) * ( 90 / (90 + 2) )

abline(v = Mode, lty = 2)

CI = qf( c(.025, .975), 10, 90)

arrows(CI[1], .05, CI[2], .05, code = 3, angle = 90, length = 1.4, col= 'red' )

points(Mode, .05, pch = 21, bg = 'green', cex = 3)

回答1:

Section 25.2 of DBDA2E gives complete R code for determining highest density intervals for distributions specified three ways: as cumulative density functions, as grid approximations, or as samples. For a cumulative density function, the function is called HDIofICDF(). It's in the utilities script, DBDA2E-utilities.R at the book's web site (linked above). Here's the code:

HDIofICDF = function( ICDFname , credMass=0.95 , tol=1e-8 , ... ) {
  # Arguments:
  # ICDFname is R’s name for the inverse cumulative density function
  # of the distribution.
  # credMass is the desired mass of the HDI region.
  # tol is passed to R’s optimize function.
  # Return value:
  # Highest density interval (HDI) limits in a vector.
  # Example of use: For determining HDI of a beta(30,12) distribution, type
  # > HDIofICDF( qbeta , shape1 = 30 , shape2 = 12 )
  # Notice that the parameters of the ICDFname must be explicitly named;
  # e.g., HDIofICDF( qbeta , 30 , 12 ) does not work.
  # Adapted and corrected from Greg Snow’s TeachingDemos package.
  incredMass = 1.0 - credMass
  intervalWidth = function( lowTailPr , ICDFname , credMass , ... ) {
    ICDFname( credMass + lowTailPr , ... ) - ICDFname( lowTailPr , ... )
  }
  optInfo = optimize( intervalWidth , c( 0 , incredMass ) , ICDFname=ICDFname ,
    credMass=credMass , tol=tol , ... )
  HDIlowTailPr = optInfo$minimum
  return( c( ICDFname( HDIlowTailPr , ... ) ,
    ICDFname( credMass + HDIlowTailPr , ... ) ) )
}

回答2:

Have you tried this package: https://github.com/robjhyndman/hdrcde ?

Following your exemple:

library(hdrcde)
hdr.den(rf(1000,10,90),prob=95)

You can use various High Density Region and it works well for mulitmodal pdf.

hdr.den(c(rf(1000,10,90),rnorm(1000,4,1)),prob=c(50,75,95))

And

And you can even use it with multivariate distribution to visual 2D high density regions:

hdrs=c(50,75,95)
x=c(rf(1000,10,90),rnorm(1000,4,1))
y=c(rf(1000,5,50),rnorm(1000,7,1) )
par(mfrow=c(1,3))
hdr.den(x,prob=hdrs,xlab="x")
hdr.den(y,prob=hdrs,xlab="y")
hdr.boxplot.2d(x,y,prob=hdrs,shadecol="red",xlab="x",ylab="y")

来源：https://stackoverflow.com/questions/42986446/determining-high-density-region-for-a-distribution-in-r

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statistics

distribution

bayesian

confidence-interval