A bivariate distribution with gamma and beta marginals with application to drought data

The first known bivariate distribution with gamma and beta marginals is introduced. Various representations are derived for its joint probability density function (pdf), joint cumulative distribution function (cdf), product moments, conditional pdfs, conditional cdfs, conditional moments, joint moment generating function, joint characteristic function and entropies. The method of maximum likelihood and the method of moments are used to derive the associated estimation procedures as well as the Fisher information matrix, variance–covariance matrix and the profile likelihood confidence intervals. An application to drought data from Nebraska is provided. Some other applications are also discussed. Finally, an extension of the bivariate distribution to the multivariate case is proposed.     

Eliminating a sparse data problem in nonparametric bivariate survival analysis with an application to women's age at first marriage and age at first birth

A new solution is proposed for a sparse data problem arising in nonparametric estimation of a bivariate survival function. Prior information, if available, can be used to obtain initial values for the EM algorithm. Initial values will completely determine estimates of portions of the distribution which are not identifiable from the data, while having a minimal effect on estimates of portions of the distribution for which the data provide sufficient information. Methods are applied to the distribution of women's age at first marriage and age at birth of first child, using data from the Current Population Surveys of 1975 and 1986.     

The relationship between double-exponential families and extended quasi-likelihood families, with application to modelling Geissler's human sex ratio data

The human sex ratio data, collected in Saxony in the 19th century by Geissler, are reanalysed by joint modelling of the mean and dispersion. Extended quasi-likelihood and the unnormalized double-exponential family are shown to lead to identical inference. The use of the unnormalized form is discussed. The relationship between multinomial and Poisson models is studied for overdispersed data.