Randomly generated lyrics using mixture models: the poem that Frank Sinatra never sang

Figures & data

Table 1. Frequency of words counts in Frank Sinatra's lyrics.

	Counts
Category	1	2	3	4	5	6
Verbs	177	99	37	32	15	17
Nouns	204	138	46	28	14	8
Adjective/Adverb (descriptive)	100	62	18	16	9	7
Other	40	43	14	14	5	7

Figure 1. Left: The solid dots depict the values of the empirical estimator of the counts of verbs occurring in the gathered lyrics of Frank Sinatra. Right: Histogram of the bootstrapped Euclidean distance between the empirical and complete monotone estimators based on the verb counts. The dashed line corresponds to the 95%-quantile of the bootstrapped distances $D_n^{\left(b\right)},b=1,\dots ,100\}$, while the solid line corresponds the observed distance $D_n$. See text for more details.

Table 2. The support points and weights of the fitted complete monotone LSE to the verb counts.

Support points ${\hat{\alpha }}_j$	0.473	0.481	0.855	0.865	0.980	0.982
Mixing probabilities ${\hat{\pi }}_j$	0.167	0.566	0.080	0.162	0.001	0.023