问题
Consider I have a million of observations following Gamma distribution with parameters (3,5). I am able to find the quantiles using summary() but I am trying to find how many observations are between each red lines which were divided into 10 pieces?
a = rgamma(1e6, shape = 3, rate = 5)
summary(a)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0053 0.3455 0.5351 0.6002 0.7845 4.4458
回答1:
We may use cut with table:
table(cut(a, quantile(a, 0:10 / 10)))
# (0.00202,0.22] (0.22,0.307] (0.307,0.382] (0.382,0.457] (0.457,0.535] (0.535,0.622]
# 99999 100000 100000 100000 100000 100000
# (0.622,0.724] (0.724,0.856] (0.856,1.07] (1.07,3.81]
# 100000 100000 100000 100000
but given what quantiles are, that may be not very interesting. Perhaps you may want to try the theoretical quantiles as well:
table(cut(a, qgamma(0:10 / 10, 3, 5)))
# (0,0.22] (0.22,0.307] (0.307,0.383] (0.383,0.457] (0.457,0.535] (0.535,0.621] (0.621,0.723]
# 99978 100114 100545 99843 99273 99644 100104
# (0.723,0.856] (0.856,1.06] (1.06,Inf]
# 100208 99883 100408
Not much more interesting since, if your data really does follow a gamma distribution and you have a bunch of observations, then you can be quite certain that there will be close to x% of data between q-th and (q+x)-th theoretical quantiles. In smaller samples the second approach can be interesting.
Edit: Given your updated question, it's clear that by 10%, 20% you don't mean quantiles. Assuming that the minimal value is 0 and the maximal is 2, if as 10% you consider 0.2, then you want
table(cut(a, seq(min(a), max(a), length = 10 + 1)))
# (0.00418,0.428] (0.428,0.853] (0.853,1.28] (1.28,1.7] (1.7,2.13] (2.13,2.55]
# 361734 436176 155332 37489 7651 1335
# (2.55,2.97] (2.97,3.4] (3.4,3.82] (3.82,4.25]
# 231 38 11 2
来源：https://stackoverflow.com/questions/54451506/how-to-calculate-the-numbers-of-the-observations-in-quantiles