Estimate the association parameter of Farlie-Gumbel-Morgenstern's bivariate distribution by maximum likelihood estimation.
The cumulative distribution function is
P(Y1 <= y1, Y2 <= y2) = y1 * y2 * ( 1 + alpha * (1 - y1) * (1 - y2) )
for -1 < alpha < 1. The support of the function is the unit square. The marginal distributions are the standard uniform distributions. When alpha=0 the random variables are independent.
An object of class
The object is used by modelling functions such as
The response must be a two-column matrix. Currently, the fitted value is a matrix with two columns and values equal to 0.5. This is because each marginal distribution corresponds to a standard uniform distribution.
T. W. Yee
Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005) Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience.
Smith, M. D. (2007) Invariance theorems for Fisher information. Communications in Statistics—Theory and Methods, 36(12), 2213–2222.
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