Alex ☆ Austria, 2015-03-17 11:19 (3299 d 22:31 ago) Posting: # 14566 Views: 6,929 |
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Dear all! I just stumbled over the generation of random draws from a truncated normal distribution whilst thinking about possible scenarios for a PK simulation study. Does anybody know how to draw from a truncated normal distribution with prespecified (fixed) mean and variance - not in the underlying normal distribution, but in the consequent truncated normal distribution? In R function truncnorm (or other functions) you can only specify the mean and sd of the underlying normal distribution... In more detail, I want to generate draws X with l < X < u ~ truncNorm(m,v) where m and v are fixed mean and variance, l=0 is the lower, u=Inf the upper bound. m and v are functions of mu and delta, the mean and variance of the underlying normal distribution N(mu,delta) without truncation. Theoretically, solving the system of equations m=f(mu,delta) and v=g(mu,delta) for mu and delta should give me the desired result, i.e. the mean and variance in the underlying normal distribution so that, after truncation, i will have mean m and variance v in the truncated normal distribution. f() and g() represent the functions describing the relationship of the mean and the variance, respectively, between normal and truncated normal distribution. As f() and g() are rather complex, including the CDF of the normal distribution, my algebraic skills are insufficient... Can anybody help? Thanks for your efforts, All the best, Alex |
Helmut ★★★ Vienna, Austria, 2015-03-17 13:48 (3299 d 20:02 ago) @ Alex Posting: # 14568 Views: 5,899 |
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Hi Alex, ❝ Theoretically, solving the system of equations m=f(mu,delta) and v=g(mu,delta) for mu and delta should give me the desired result […] my algebraic skills are insufficient... Not only yours. Consider contacting the authors of truncnorm Heike Trautmann <trautmannstatistik.uni-dortmund.de> — Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
ElMaestro ★★★ Denmark, 2015-03-17 16:20 (3299 d 17:31 ago) @ Alex Posting: # 14569 Views: 5,752 |
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Hi Alex, ❝ Does anybody know how to draw from a truncated normal distribution with prespecified (fixed) mean and variance - not in the underlying normal distribution, but in the consequent truncated normal distribution? In R function truncnorm (or other functions) you can only specify the mean and sd of the underlying normal distribution... Never did something like that. I believe you can get the relationship between underlying mean and variance and truncated mean and variance here. Perhaps this relation is what you need to draw appropriately for your application. — Pass or fail! ElMaestro |
nobody nothing 2015-03-17 16:24 (3299 d 17:26 ago) @ ElMaestro Posting: # 14570 Views: 5,712 |
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eeehhm, stupid question: Why not "sampling" on the log scale for your simulations and transform afterwards? Or do I get something completely wrong here? — Kindest regards, nobody |
Alex ☆ Austria, 2015-03-17 16:56 (3299 d 16:54 ago) @ nobody Posting: # 14571 Views: 5,659 |
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Dear all! Thanks for your fast responses. @Helmut: Thanks for the hint, I just contacted the authors of the package. @ElMaestro: Thanks. Relationships are known (but complex). I tried to invert the equations by using the substitution mehtod without success. I was just surprised that the web showed no solution.. @nobody: Of course, a log-normal distribution is another possible scenario. And in fact its the same issue with function lnorm in R: you can only specify mean and sd for the underlying normal distribution. BUT: Relationships for mean and variance are much simpler between normal and log-normal distribution and therefore, solving is not that tricky: rlnorm(n=n, meanlog=log(mu)-0.5*log(1+cv^2), sdlog=sqrt(log(1+cv^2))) where mu and cv represent the mean and the cv for the resulting log-normal distribution (not for the underlying normal distribution). Thanks again, Alex |