Kumaraswamy Regression Family Function
Estimates the two parameters of the Kumaraswamy distribution by maximum likelihood estimation.
kumar(lshape1 = "loglink", lshape2 = "loglink",
ishape1 = NULL, ishape2 = NULL, gshape1 = exp(2*ppoints(5) - 1),
tol12 = 1.0e-4, zero = NULL)lshape1, lshape2 |
Link function for the two positive shape parameters,
respectively, called a and b below.
See |
ishape1, ishape2 |
Numeric. Optional initial values for the two positive shape parameters. |
tol12 |
Numeric and positive. Tolerance for testing whether the second shape parameter is either 1 or 2. If so then the working weights need to handle these singularities. |
gshape1 |
Values for a grid search for the first shape parameter.
See |
zero |
The Kumaraswamy distribution has density function
a*b*y^(a-1)*(1-y^a)^(b-1)
where 0 < y < 1 and the two shape parameters, a and b, are positive. The mean is b * Beta(1+1/a,b) (returned as the fitted values) and the variance is b * Beta(1+2/a,b) - (b * Beta(1+1/a,b))^2. Applications of the Kumaraswamy distribution include the storage volume of a water reservoir. Fisher scoring is implemented. Handles multiple responses (matrix input).
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
T. W. Yee
Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46, 79–88.
Jones, M. C. (2009). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6, 70–81.
shape1 <- exp(1); shape2 <- exp(2) kdata <- data.frame(y = rkumar(n = 1000, shape1, shape2)) fit <- vglm(y ~ 1, kumar, data = kdata, trace = TRUE) c(with(kdata, mean(y)), head(fitted(fit), 1)) coef(fit, matrix = TRUE) Coef(fit) summary(fit)
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