View source: R/family.mixture.R
mix2exp  R Documentation 
Estimates the three parameters of a mixture of two exponential distributions by maximum likelihood estimation.
mix2exp(lphi = "logitlink", llambda = "loglink", iphi = 0.5,
il1 = NULL, il2 = NULL, qmu = c(0.8, 0.2), nsimEIM = 100,
zero = "phi")
lphi, llambda 
Link functions for the parameters 
iphi, il1, il2 
Initial value for 
qmu 
Vector with two values giving the probabilities relating to the
sample quantiles for obtaining initial values for

nsimEIM, zero 
See 
The probability density function can be loosely written as
f(y) = \phi\,Exponential(\lambda_1) +
(1\phi)\,Exponential(\lambda_2)
where \phi
is the probability an observation belongs
to the first group, and y>0
.
The parameter \phi
satisfies
0 < \phi < 1
.
The mean of Y
is
\phi / \lambda_1 + (1\phi) / \lambda_2
and this is returned as the fitted values.
By default, the three linear/additive predictors are
(logit(\phi), \log(\lambda_1), \log(\lambda_2))^T
.
An object of class "vglmff"
(see vglmffclass
).
The object is used by modelling functions
such as vglm
and vgam
.
This VGAM family function requires care for a successful
application.
In particular, good initial values are required because
of the presence of local solutions. Therefore running
this function with several different combinations of
arguments such as iphi
, il1
, il2
,
qmu
is highly recommended. Graphical methods such
as hist
can be used as an aid.
This VGAM family function is experimental and should be used with care.
Fitting this model successfully to data can be
difficult due to local solutions, uniqueness problems
and illconditioned data. It pays to fit the model
several times with different initial values and check
that the best fit looks reasonable. Plotting the
results is recommended. This function works better as
\lambda_1
and \lambda_2
become more different. The default control argument
trace = TRUE
is to encourage monitoring convergence.
T. W. Yee
rexp
,
exponential
,
mix2poisson
.
## Not run: lambda1 < exp(1); lambda2 < exp(3)
(phi < logitlink(1, inverse = TRUE))
mdata < data.frame(y1 = rexp(nn < 1000, lambda1))
mdata < transform(mdata, y2 = rexp(nn, lambda2))
mdata < transform(mdata, Y = ifelse(runif(nn) < phi, y1, y2))
fit < vglm(Y ~ 1, mix2exp, data = mdata, trace = TRUE)
coef(fit, matrix = TRUE)
# Compare the results with the truth
round(rbind('Estimated' = Coef(fit),
'Truth' = c(phi, lambda1, lambda2)), digits = 2)
with(mdata, hist(Y, prob = TRUE, main = "Orange=estimate, blue=truth"))
abline(v = 1 / Coef(fit)[c(2, 3)], lty = 2, col = "orange", lwd = 2)
abline(v = 1 / c(lambda1, lambda2), lty = 2, col = "blue", lwd = 2)
## End(Not run)
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