Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some importan...

In this article we construct bivariate discrete distribution in Z. We make use of a generalized trivariate reduction technique. The special case leading to bivariate Skellam distributions is studied in detail. Properties of the derived models as well as estimation are examined. Real data application is provided. Discussion of extensions to different models is also mentioned.

In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire inte...

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

1. Residues . ..... ........ .... ... .... 54 2. ir-discrete distributions ............... . .. . . .. . 58 3. Admissible families of operators .......... ............. 67 4. The main formula ............. ... ............ 74 5. Completion of the induction argument .................... 83 6. Cuspidal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7. Conclusions ..............

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its nite-dimensional distributions. This is applied to characterize residual allocation models with independent factors that are invariant under size-biased permutation. Apart from some exceptional cases and minor modiications, such models form a two-parameter fami...

This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are inves...

We derive useful distributional representations for three discrete laws: the discrete stable distribution of Steutel and Van Ham, the discrete Linnik distribution introduced by Pakes, and a distribution of Sibuya. These representations may be used to obtain simple uniformly fast random variate generators. AMS 1991 Subject Classifications: 65C10, 68505.

We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which will have uniformly minimum variance unbiased estimators with finite variance are explicitly characterized. The general result allows us to construct a large nu...

Making use of the pullbacks, we reformulate the following quadratic functional equation: f x y z f x f y f z f x y f y z f z x in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperf...