Journal of Iranian Statistical Society
Volume:14 Issue: 2, 2015

We introduce a new five-parameter distribution called the beta exponentiated Gumbel (BEG) distribution that includes the beta Gumbel, exponentiated Gumbel and Gumbel distribution. Expressions for the distribution function, density function and rth moment of the new distribution and order statistics are obtained. We discuss estimation of the parameters by maximum liklelihood and provide the information matrix. Using a real data set, we observe that the BEG distribution is flexible and can be used quite effectively in analysing positive data in place of the special cases.

ýRecently a first-order Spatial Integer-valued Autoregressiveý ýSINAR(1,1) model was introduced to model spatial data that comesý ýin counts citep{ghodsi2012}ý. ýSome properties of this modelý ýhave been established and the Yule-Walker estimator has beený ýproposed for this modelý. ýIn this paperý, ýwe introduce theý ýconditional maximum likelihood method for estimating theý ýparameters of the Poisson SINAR(1,1) modelý. ýThe asymptoticý ýdistribution of the estimators are also derivedý. ýThe properties ofý ýthe Yule-Walker and conditional maximum likelihood estimators areý ýcompared by simulation studyý. ýFinallyý, ýthe Student data citep{student1906} oný ýthe yeast cells count are used to illustrate the fitting of theý ýSINAR(1,1) modelý.

ýMultivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie modelsý. ýThe model is composed of a univariate Poisson variableý, ýand the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson componentý. ýTwo characterizations of this model are showný, ýfirst by variance function and then by generalized variance function which is the determinant of the variance functioný. ýThe latter provides an explicit solution of a particular Monge-Ampère equation.

In this paperý, ýwe consider the problem of estimating E(Y) based on a simple random sample when at least one of the population quantiles is knowný. ýWe propose a stratified estimator of E(Y)ý, ýand show that it is strongly consistentý. ýWe then establish the asymptotic normality of the suggested estimatorý, ýand prove that it is asymptotically more efficient than the standard mean estimator in simple random samplingý. ýFor finite sample sizesý, ýMonte Carlo simulation is used to show that the proposed method considerably improves the standard procedureý. ýFinallyý, ýa real data example is used to illustrate the application of the proposed methodý.

Here we consider a new class of skew logistic distribution as a generalized mixture of the standard logistic and skew logistic distributionsý, ýand study some of its important aspectsý. ýThe tail behaviour of the distribution is compared with that of the skew logistic distribution and a location-scale extension of the distribution is proposedý. ýFurther the maximum likelihood estimation of the parameters of the extended class of distribution is attempted. The usefulness of the proposed class of distribution is illustrated with the help of a data setý.

Several modifications of the Laplace distribution have been introduced and applied in various fields up to this dayý. ýIn this paperý, ýwe introduce a modified symmetric version of the classical Laplace distributioný. ýWe provide a comprehensive theoretical description of this distributioný. ýIn particularý, ýwe derive the formulas for the $k$th momentý, ýquantiles and several useful alternative representations of the distributioný. ýWe derive the maximum likelihood estimators of the parameters and investigate their properties via simulationý. ýFinallyý, ýwe analyse three real-world datasets to illustrate the usefulness of the modified classical Laplace distributioný. ýThe results suggest that further improvement to classical Laplace distribution fitting is possible and the new model provides an attractive alternative to the classical Laplace distribution.