Complementary lognormal_cdf(reals y, reals mu, reals sigma)

Modeling
1

I want to customize my likelihood function. In my customized LL, I need the lognormal complementary cumulative distribution function of y. I cannot use lognormal_lccdf as it is the log of what I need. I cannot use 1-lognormal_cdf as I get an error as shown below:

target += 1 -lognormal_cdf(t_0_0_1 | mu_0_0_1, sigma1)

PARSER EXPECTED: "("
Error in stanc(filename, allow_undefined = TRUE) : 
  failed to parse Stan model '0 Copula-Base' due to the above error.

Would you please advise which function I can use?

2

Could you use exp(lognormal_lccdf)?

3

Thank you very much for your reply. I ended up doing that but I was wondering if a direct function is available? Is this method efficient?

4

No there isn’t a direct function available, so this is likely to be your best bet

5

Good to know. Thanks.

6

Would you please let me know why

target += 1 -lognormal_cdf(t_0_0_1 | mu_0_0_1, sigma1)

is not valid and results in the following error?

PARSER EXPECTED: "("
Error in stanc(filename, allow_undefined = TRUE) : 
  failed to parse Stan model '0 Copula-Base' due to the above error.
7

Just checking–it’s not a matter of missing a semicolon at the end of the line, is it?

8

Thank you for the reply. But, no it is not. The error occurs with and without the semicolon

9

That PARSER EXPECTED sounds like you’re using an older RStan. Vertical bar notation has not always been applied consistently, try with a comma instead.

target += 1 -lognormal_cdf(t_0_0_1, mu_0_0_1, sigma1)
10

Thank you for your response, @nhuurre.
You are absolutely right.

1 -lognormal_cdf

does not work with vertical bar notation, but it works with a comma.

Based on this I expect to see the same result by these two lines of code:

target += (1-lognormal_cdf(t_0_0_1 , mu_0_0_1, sigma1));
target += exp(lognormal_lccdf(t_0_0_1 | mu_0_0_1, sigma1));

However, based on my experiment they result in two different values. Here is how they are calculated:
The first one → calculates CDF for each row and then multiplies all of them. then, subtracts it from 1.
The second one → calculates log(1-CDF) for each row and sums all of them. Then, calculates the exp of it.

I understand how and why the second one works correctly (log(s1) + log(s2) = log(s1.s2)). However, I don’t understand why lognormal_cdf multiplies all CDF values and does not add them?

Would you please tell me how it works?

11

A CDF produces a probability and combining independent events to a joint event multiplies their probabilities. Why would you want to add probabilities?
And wait, why does your customized LL (log-likelihood) need a CDF instead of a log-CDF?

12

Right
Thanks, @nhuurre

My likelihood function contains terms like: (S1+S2)^a, which makes Loglikelihood of a.log(S1+S2).

I think for what I want exp(lccdf(.)) is correct and not 1-cdf(.), right?

Maybe both are wrong and I should use a loop rather than vectorization?