R. I have a vector with values. I would like to implement a formula that uses CDF and PDF

Question

Suppose that I have a vector with values, for example:

MyVector=(99,100,100,98,99,101,99,101,102,100)

From here I would like to use a formula that would give me CDF(x)/PDF(x) for those values of x that are defined. I can use the function ecdf to get the numerator:

MyCDF <- ecdf(MyVector)

Then I would be able to write, say, MyCDF(100) which would give me 0.7 as the result.

But it looks like there is no similar function for PDF (the denominator)?

As a result I would like to be able to get the following table in the example above:

Value	PDF	CDF	CDFdivPDF
98	0.1	0.1	1
99	0.3	0.4	1.33
100	0.3	0.7	2.33
101	0.2	0.9	4.5
102	0.1	1	10

Also, I would like to make a plot where values are on the x-axis, and PDF, CDF, CDFdivPDF are plotted.

Could you please help? Thank you in advance!

Answer 1

You should use ecdf like below

x <- sort(unique(MyVector))
cdf <- ecdf(MyVector)(x)
pdf <- diff(c(0, cdf))

data.frame(
    value = x,
    CDF = cdf,
    PDF = pdf,
    CDFdivPDF = cdf / pdf
)

such that

  value CDF PDF CDFdivPDF
1    98 0.1 0.1  1.000000
2    99 0.4 0.3  1.333333
3   100 0.7 0.3  2.333333
4   101 0.9 0.2  4.500000
5   102 1.0 0.1 10.000000