Prentice (1974) Log-gamma Distribution
Estimation of a 3-parameter log-gamma distribution described by Prentice (1974).
prentice74(llocation = "identitylink", lscale = "loglink",
lshape = "identitylink", ilocation = NULL, iscale = NULL,
ishape = NULL, imethod = 1,
glocation.mux = exp((-4:4)/2), gscale.mux = exp((-4:4)/2),
gshape = qt(ppoints(6), df = 1), probs.y = 0.3,
zero = c("scale", "shape"))llocation, lscale, lshape |
Parameter link function applied to the
location parameter a,
positive scale parameter b
and the shape parameter q, respectively.
See |
ilocation, iscale |
Initial value for a and b, respectively. The defaults mean an initial value is determined internally for each. |
ishape |
Initial value for q. If failure to converge occurs, try some other value. The default means an initial value is determined internally. |
imethod, zero |
See |
glocation.mux, gscale.mux, gshape, probs.y |
See |
The probability density function is given by
f(y;a,b,q) = |q| * exp(w/q^2 - e^w) / (b*gamma(1/q^2)),
Special cases: q = 0 is the normal distribution with standard deviation b, q = -1 is the extreme value distribution for maximums, q = 1 is the extreme value distribution for minima (Weibull). If q > 0 then the distribution is left skew, else q < 0 is right skew.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
The special case q = 0 is not handled, therefore estimates of q too close to zero may cause numerical problems.
The notation used here differs from Prentice (1974): alpha = a, sigma = b. Fisher scoring is used.
T. W. Yee
Prentice, R. L. (1974). A log gamma model and its maximum likelihood estimation. Biometrika, 61, 539–544.
pdata <- data.frame(x2 = runif(nn <- 1000)) pdata <- transform(pdata, loc = -1 + 2*x2, Scale = exp(1)) pdata <- transform(pdata, y = rlgamma(nn, loc = loc, scale = Scale, shape = 1)) fit <- vglm(y ~ x2, prentice74(zero = 2:3), data = pdata, trace = TRUE) coef(fit, matrix = TRUE) # Note the coefficients for location
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