Maximum likelihood estimation of the 2-parameter Lomax distribution.
lomax(lscale = "loglink", lshape3.q = "loglink", iscale = NULL, ishape3.q = NULL, imethod = 1, gscale = exp(-5:5), gshape3.q = seq(0.75, 4, by = 0.25), probs.y = c(0.25, 0.5, 0.75), zero = "shape")
Parameter link function applied to the
The 2-parameter Lomax distribution is the 4-parameter generalized beta II distribution with shape parameters a=p=1. It is probably more widely known as the Pareto (II) distribution. It is also the 3-parameter Singh-Maddala distribution with shape parameter a=1, as well as the beta distribution of the second kind with p=1. More details can be found in Kleiber and Kotz (2003).
The Lomax distribution has density
f(y) = q / [b (1 + y/b)^(1+q)]
for b > 0, q > 0, y >= 0.
Here, b is the scale parameter
q is a shape parameter.
The cumulative distribution function is
F(y) = 1 - [1 + (y/b)]^(-q).
The mean is
E(Y) = b/(q-1)
provided q > 1; these are returned as the fitted values. This family function handles multiple responses.
An object of class
The object is used by modelling functions such as
See the notes in
T. W. Yee
Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.
ldata <- data.frame(y = rlomax(n = 1000, scale = exp(1), exp(2))) fit <- vglm(y ~ 1, lomax, data = ldata, trace = TRUE) coef(fit, matrix = TRUE) Coef(fit) summary(fit)
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