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Generating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases. [ABSTRACT FROM AUTHOR]

This article considers a unified approach based on the mixture method to construct linear bivariate models and those on the cylinder and torus involving the exponential and cardioid distributions with the truncated exponential distribution as the mixing distribution. Parameter estimation of the bivariate model on the torus is considered for the data set of phase angles of circadian-related genes in heart and liver tissues. [ABSTRACT FROM AUTHOR]

This article considers a probability generating function-based divergence statistic for parameter estimation. The performance and robustness of the proposed statistic in parameter estimation is studied for the negative binomial distribution by Monte Carlo simulation, especially in comparison with the maximum likelihood and minimum Hellinger distance estimation. Numerical examples are given as illustration of goodness of fit. [ABSTRACT FROM AUTHOR]

This article considers a discrete distribution that arises as the dominant solution of a linear difference equation. Basic properties and various chance mechanisms that lead to this distribution are given. In particular, its formulation as a weighted distribution and a mixed Poisson process are proposed. Parameter estimation by (a) using a combination of observed frequencies and moments and (b) maximum likelihood are examined. An example of goodness of fit is considered. [ABSTRACT FROM AUTHOR]

A new generalization of the logarithmic distribution (LD)—the generalized logarithmic distribution (GLD)—is introduced. The GLD is a cluster size distribution of the inverse trinomial distribution, which arises in a generalized random walk problem. Major properties of the GLD are derived and discussed. The method of first moment and frequency of one count and maximum likelihood estimation (MLE) are used for parameter estimation. Rao's score test statistic is derived as a model selection tool. Finally, we demonstrate an application of the GLD in fitting insect data from temperate and tropical regions. [ABSTRACT FROM AUTHOR]