Random Samples from Cauchy Distribution

Description

The data set is used to understand the sampling variation of the score function. The simulated data is available in Pawitan (2001).

Usage

data(cs)

Format

A data frame with 10 observations on the following 20 variables.

Sample.1

a numeric vector

Sample.2

a numeric vector

Sample.3

a numeric vector

Sample.4

a numeric vector

Sample.5

a numeric vector

Sample.6

a numeric vector

Sample.7

a numeric vector

Sample.8

a numeric vector

Sample.9

a numeric vector

Sample.10

a numeric vector

Sample.11

a numeric vector

Sample.12

a numeric vector

Sample.13

a numeric vector

Sample.14

a numeric vector

Sample.15

a numeric vector

Sample.16

a numeric vector

Sample.17

a numeric vector

Sample.18

a numeric vector

Sample.19

a numeric vector

Sample.20

a numeric vector

References

Pawitan, Y. (2001). In All Likelihood. Oxford Science Publications.

Examples

data(cs)
n <- 10
cauchy_score_fn  <-  function(mu,x)
      sum(2*(x-mu)/(1+(x-mu)^{2}))
mu <- seq(from=-15,to=20,by=0.5)
plot(mu,sapply(mu,cauchy_score_fn,x=cs[,1]),"l",xlab=expression(mu),
ylab=expression(S(mu)),ylim=c(-10,10))
title(main="D: Score Function Plot of Cauchy Model")
for(i in 2:20) lines(mu,sapply(mu,
cauchy_score_fn,x=cs[,i]),"l")
abline(v=4)
abline(h=0)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
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> library(ACSWR)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ACSWR/cs.Rd_%03d_medium.png", width=480, height=480)
> ### Name: cs
> ### Title: Random Samples from Cauchy Distribution
> ### Aliases: cs
> ### Keywords: Cauchy random samples, score function
> 
> ### ** Examples
> 
> data(cs)
> n <- 10
> cauchy_score_fn  <-  function(mu,x)
+       sum(2*(x-mu)/(1+(x-mu)^{2}))
> mu <- seq(from=-15,to=20,by=0.5)
> plot(mu,sapply(mu,cauchy_score_fn,x=cs[,1]),"l",xlab=expression(mu),
+ ylab=expression(S(mu)),ylim=c(-10,10))
> title(main="D: Score Function Plot of Cauchy Model")
> for(i in 2:20) lines(mu,sapply(mu,
+ cauchy_score_fn,x=cs[,i]),"l")
> abline(v=4)
> abline(h=0)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>