Description Usage Arguments Details Value Acknowledgement Author(s) References Examples

Density, distribution function, quantile function and random variate generation for the 28 distributions from Berlinet/Devroye (1994).

1 2 3 4 |

`dnum` |
number of distribution as in Berlinet/Devroye (1994), Section 3.2. |

`x,q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. |

These functions implement the 28 distributions from Berlinet and Devroye (1994), Section 3.2, which are:

`dnum == 1`

"uniform" on [0,1] as in stats-package

`dnum == 2`

"exponential" as in stats-package

`dnum == 3`

"Maxwell"

`dnum == 4`

"double exponential"

`dnum == 5`

"logistic" as in stats-package

`dnum == 6`

"Cauchy" as in stats-package

`dnum == 7`

"extreme value"

`dnum == 8`

"infinite peak"

`dnum == 9`

"Pareto"

`dnum == 10`

"symmetric Pareto"

`dnum == 11`

"normal" as in stats-package

`dnum == 12`

"lognormal"

`dnum == 13`

"uniform scale mixture"

`dnum == 14`

"Matterhorn"

`dnum == 15`

"logarithmic peak"

`dnum == 16`

"isosceles triangle"

`dnum == 17`

"beta 2,2" as in stats-package

`dnum == 18`

"chi-square 1" as in stats-package

`dnum == 19`

"normal cubed"

`dnum == 20`

"inverse exponential"

`dnum == 21`

"Marronite"

`dnum == 22`

"skewed bimodal"

`dnum == 23`

"claw"

`dnum == 24`

"smooth comb"

`dnum == 25`

"caliper"

`dnum == 26`

"trimodal uniform"

`dnum == 27`

"sawtooth"

`dnum == 28`

"bilogarithmic peak"

`dberdev` |
gives the density, |

`pberdev` |
gives the distribution function, |

`qberdev` |
gives the quantile function, and |

`rberdev` |
generates random deviates. |

The authors thank Luc Devroye for providing his original implementation for testing purposes.

Thoralf Mildenberger, Henrike Weinert and Sebastian Tiemeyer

A. Berlinet and L. Devroye, "A comparison of kernel density estimates," Publications de l'Institut de Statistique de l'Universite de Paris, vol. 38(3), pp. 3-59, 1994. http://cg.scs.carleton.ca/~luc/devs.html

T. Mildenberger and H. Weinert, "The benchden Package: Benchmark Densities for Nonparametric Density Estimation", Journal of Statistical Software, vol. 46(14), 1-14, 2012. http://www.jstatsoft.org/v46/i14/

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# histogram and true density of "Claw"-distribution
hist(rberdev(1000,dnum=23),breaks=100, main = " ",freq=FALSE)
lines(seq(-3,3,0.01),dberdev(seq(-3,3,0.01),dnum=23),col="blue",lwd=2)
title(paste(nberdev(dnum=23)))
# plot cdf of simulated data and the df of "Matterhorn"-distribution
plot.stepfun(rberdev(100,dnum=14),do.points=TRUE,main="")
lines(seq(-1,1,0.001),pberdev(seq(-1,1,0.001),dnum=14),col="blue")
title(paste(nberdev(dnum=14)))
# plot quantiles of "smooth comb"-distribution
plot(qberdev(seq(0,1,0.01),dnum=24),t="l")
title(paste(nberdev(dnum=24)))
``` |

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