In this paper, we study the limit properties of the ratio for order statistics based on samples from an exponential distribution and obtain the expression of the density functions, the existence of the moments, the strong law of large numbers for [Formula: see text] with [Formula: see text]. We also discuss other limit theorems such as the central limit theorem, the law of iterated logarithm, t...

We define the class of bivariate binomial distributions as Poisson distributions transformed by a binomial dilution and mixing with a gamma distribution. They are used to study the number of nematodes, considering the sex ratio, parasitizing birds.

Penna (2011) asks whether subjects with different follow-up times can be analysed through binomial regression. The answer to this question is “yes”. If the rate for a particular person is λ and they have been observed for a period of time (t), then the probability (p) of having an event during that time is equal to 1-e-λt. The equation can be re-arranged to give log[log(1-p)] = log(λ)+log(t). T...

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates cr...