Here is my findings:
N <- 100
mu <- 1
sigma <- 2
gamma <- 3
set.seed(42)
x <- rlnorm(N, mu, sigma) + gamma
min(x)
[1] 3.006832
foo <- function(x, mu, sigma, gamma)
+ {dlnorm(x - gamma, mu, sigma)}
## min(x) is not the right upper bound to use for gamma
fit <- fitdistr(x, densfun = foo,
+ start = list(mu = 0.9, sigma = 1.9, gamma = 2.9),
+ lower = c(-Inf, 0, -Inf),
+ upper=c(Inf, Inf, min(x)))
Error in stats::optim(x = c(45.178764955739, 3.87862565957867,
8.61957940802123, :
L-BFGS-B needs finite values of 'fn'
## now upper bound for gamma is not to large
fit <- fitdistr(x, densfun = foo,
+ start = list(mu = 0.9, sigma = 1.9, gamma = 2.9),
+ lower = c(-Inf, 0, -Inf),
+ upper=c(Inf, Inf, 3))
fit
mu sigma gamma
1.08694600 2.02546254 2.99393215
(0.20902998) (0.17736860) (0.01663611)
## now upper bound for gamma is not to large
## still able to find correct estimates for parameters for other start values
fit <- fitdistr(x, densfun = foo,
+ start = list(mu = 0, sigma = 1, gamma = 0),
+ lower = c(-Inf, 0.0001, -Inf),
+ upper=c(Inf, Inf, 3))
fit
mu sigma gamma
1.08671881 2.02579806 2.99394094
(0.20907178) (0.17745706) (0.01663591)
## Nelder-Mead method seems to do the job
fit <- fitdistr(x, densfun = foo, method = "Nelder-Mead",
start = list(mu = 0, sigma = 1, gamma = 0))
fit
mu sigma gamma
1.08678997 2.02571374 2.99393924
(0.20906041) (0.17743258) (0.01663503)
## these two functions are defined and used in the code for fitdistr
## myfn is the objective function to be optimized in optim()
dens <- function(parm, ...) foo(x, parm, ...)
myfn <- function(parm, ...) -sum(log(dens(parm, ...)))
## for gamma > 3. Here min(x) = 3.006832
## have at least one illegal value of log-normal
table(dens(1, 2, min(x)) > 0)
FALSE TRUE
1 99
## resulting in
myfn(0.9, 1.9, min(x))
[1] Inf
## but for gamma = 3 we get finite likelihood
myfn(0.9, 1.9, 3.000000)
[1] 322.4375
## also finite likelihood
myfn(0.9, 1.9, -3.000000)
[1] 456.7857
Yours sincerely / Med venlig hilsen
Frede Aakmann Tøgersen
Specialist, M.Sc., Ph.D.
Plant Performance & Modeling
Technology & Service Solutions
T +45 9730 5135
M +45 2547 6050
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-----Original Message-----
From: Rolf Turner [mailto:r.tur...@auckland.ac.nz]
Sent: 17. januar 2014 22:47
To: Vito Ricci
Cc: Frede Aakmann Tøgersen; Göran Broström; r-h...@stat.math.ethz.ch
Subject: Re: [R] Estimating parameters of 3 parameters lognormal
distribution
Can you please tell us (me!) how you chose starting values?
Out of curiosity I tried the following:
set.seed(42)
x <- rlnorm(100,1,2) + 3
require(MASS)
strt <- list(mu=1,sigma=2,gamma=3)
fit <- fitdistr(x,densfun=function(x,mu,sigma,gamma)
{dlnorm(x-gamma,mu,sigma)
},
start=strt,lower=c(0,0,-Inf),
upper=c(Inf,Inf,min(x)))
and it ran just fine and gave sensible answers. But when I took:
strt <- list(mu=0.9,sigma=1.9,gamma=2.9)
(not very different from the previous starting values)
I got an error:
Error in stats::optim(x = c(45.178764955739, 3.87862565957867,
8.61957940802123, :
L-BFGS-B needs finite values of 'fn'
On 18/01/14 01:00, Vito Ricci wrote:
OK. It runs fine! Many thanks Frede.
Regards.
Vito
Se non ora, quando?
Se non qui, dove?
Se non tu, chi?
Il Venerdì 17 Gennaio 2014 12:38, Frede Aakmann Tøgersen
<fr...@vestas.com> ha scritto:
In package MASS there is the fitdistr function using maximum likelihood
estimation to infer on the parameters of distributions based on observed
data.
One of the arguments of fitdistr () allows you to specify the probability
density function.
You only know how the parametrization of your three parameters
lognormal distribution is defined since you really haven't told us much.
Please have a look at fitdistr() and tell us if fit your needs.
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