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Inference methods for the positive stable laws, which have no closed form expression for the density functions are developed based on a special quadratic distance using negative moments. Asymptotic properties of the quadratic distance estimator (QDE) are established. The QDE is shown to have asymptotic relative efficiency close to 1 for almost all the… (More)

Goodness of fit test procedures for the zeta parametric family based on quadratic distances and the Box--Cox transform are developed. Test statistics based on quadratic distances are shown to follow a chi-square distribution asymptotically. Test procedures based on the Box-Cox transform make use of the estimator of the parameter introduced by the Box-Cox… (More)

- Louis G. Doray, Shu Mei Jiang, Andrew Luong
- Communications in Statistics - Simulation and…
- 2009

In this paper, we develop a method to estimate the two parameters of the discrete stable distribution. By minimizing the quadratic distance between transforms of the empirical and theoretical probability generating functions, we obtain estimators simple to calculate, asymptotically unbiased and normally distributed. We also derive the expression for their… (More)

The zeta distribution with regression parameters has been rarely used in statistics because of the difficulty of estimating the parameters by traditional maximum likelihood. We propose an alternative method for estimating the parameters based on an iteratively reweighted least-squares algorithm. The quadratic distance estimator (QDE) obtained is consistent,… (More)

- Louis G. Doray
- 2009

We consider the problem of estimating the three parameters of the bivariate Poisson distribution. From the recursive expression for the probability mass function, which is linear in its parameters, we develop the quadratic distance estimator (QDE), which can be computed with an iteratively reweighted least-squares algorithm. The QDE is unbiased, easy to… (More)

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