multimode (version 1.0)

stamps: Stamps thickness

Description

This dataset, analysed in Izenman and Sommer (1988) and Ameijeiras--Alonso et al. (2017), consists of thickness measurements (in millimeters) of 485 unwatermarked used white wove stamps of the 1872 Hidalgo stamp issue of Mexico. All of them had an overprint with the year (1872 or either an 1873 or 1874) and some of them were watermarked (Papel Sellado or LA+-F).

Usage

data(stamps)
data(stamps1)
data(stamps2)
data(stampstable)

Format

stamps includes the thickness (in millimeters) of the different stamps in the 1872 Hidalgo stamp issue. stamps1 includes both the thickness and the overprinted year. stamps2 includes both the thickness and the watermark. stampstable reproduces the original frequency table in Izenman and Sommer (1988), including the thickness, the overprinted years (1872 or 1873-1874) and the watermarks (Papel Sellado or LA+-F).

Details

This is a classic example for determining the number of modes.

References

Ameijeiras--Alonso, J., Crujeiras, R.M. and Rodr<U+00ED>guez--Casal, A. (2016). Mode testing, critical bandwidth and excess mass, arXiv preprint: 1609.05188.

Izenman, A. J., and Sommer, C. J. (1988). Philatelic mixtures and multimodal densities. Journal of the American Statistical association, 83, 941--953.

Examples

# NOT RUN {
data("stamps")
# Histogram of Wilson (bin width 0.008)
seqx=seq(0.0585,0.1385,by=0.008)
hist(stamps,breaks=seqx)
# Histogram of Figure 1, Izenman and Sommer (bin width 0.002)
seqx=seq(0.0585,0.1385,by=0.002)
hist(stamps,breaks=seqx)

# Kernel density estimation of Izenman and Sommer (number of modes: 7)
locmodes(stamps,mod0=7,lowsup=0.04,uppsup=0.15,display=TRUE)
# Kernel density estimation of Ameijeiras-Alonso et al. (number of modes: 4)
locmodes(stamps,mod0=4,lowsup=0.04,uppsup=0.15,display=TRUE)

# }