你可以在带宽向量上循环

> bw <- seq.int(.02, .5, len=100)
> r <- sapply(bw, \(i) multimode::nmodes(x, i))
> plot(r, log='y', type='s', yaxt='n'); axis(2, 1:1e5)

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并以图形方式评估

它建议了三种模式，因为从3到下一个更高的数字的步长是“非常高的”。也许你可以使用95%quantile，但即使这样也不能提供太多的保护来防止任意性。

> n_mod <- quantile(r, .95)
> mm <- multimode::locmodes(x, mod0=n_mod)
Warning message:
In multimode::locmodes(x, mod0 = n_mod) :
  If the density function has an unbounded support, artificial modes may have been created in the tails
> multimode::locmodes(x, mod0=n_mod, display=TRUE)

Estimated location
Modes: 0.1222717  0.853707   1.24139 
Antimodes: 0.4918366  1.060701 

Estimated value of the density
Modes:   4.4179  0.3331802  3.866845 
Antimodes: 8.326824e-13  0.001885466 

Critical bandwidth: 0.0383606

Warning message:
In multimode::locmodes(x, mod0 = n_mod, display = TRUE) :
  If the density function has an unbounded support, artificial modes may have been created in the tails

型

multimode::sizer还建议了三种模式，请查看?multimode::sizer的参考资料，了解它们是如何确定的：

> summary(multimode::sizer(x, display=FALSE))

The estimated modes are located between the following values
(for the log10 bandwidths range indicated in parenthesis)

Mode 1:  0.10288 | 0.649395 (-1.672682 0.09191453)
Mode 2:  1.009708 | 1.253947 (-1.672682 -0.3487716)
Mode 3:  0.7920692 | 0.9226525 (-1.205673 -1.061009)

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• 数据：*

set.seed(123)
x <- c(rnorm(250, 0.125, 0.03), rnorm(25, 0.85, 0.05), rnorm(200, 1.24, 0.02))

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一个快速而肮脏的方法是找到内核密度的峰值：

with(density(x, bw = 0.05), x[which(diff(sign(diff(y))) == -2) + 1])
#> [1] 0.1221060 0.8584025 1.2400746

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注意，这给出了与locmodes几乎相同的结果。
将bw参数设置为更高的值是一种平滑噪声的方法。它需要一些图形探索来找到正确的值。