The class of discrete distributions supported on the setup integers is considered. A discrete version of normal distribution can be characterized via maximum entropy. Also, moments, Shannon entropy and Renyi entropy have obtained for discrete symmetric distribution. It is shown that the special cases of this measures imply the discrete normal and discrete Laplace distributions. Then, an analogue of Fisher information is studied by discrete normal, bilateral power series, symmetric discrete and double logarithmic distributions. Also, the conditions under which the above distributions are unimodal are obtained. Finally, central and non-central moments, entropy and maximum entropy of double logarithmic distribution have achieved.

This paper explores the optimal criterion for comparison of some Phi-divergence measures. The dependence for generalized Farlie Gumbel Morgenstern family of copulas is numerically calculated and it has been shown that the Hellinger measure is the optimal criterion for measuring the divergence from independence.

In the individual risk processes of an insurance company with dependent claim sizes, determination of the ruin probability and time to ruin are very important. Exact computing of theses probabilities, because of it's complex structure, is not easy. In this paper, Monte Carlo simulation method is used to obtain the ruin probabilities estimates, times to ruin and confidence interval for the ruin probability estimates of the mentioned process for different dependence level of claims. In this simulation the multivariate Frank copula function and Marshall and Olkin's algorithm are provided to generate the dependent claims. Then it has shown that with increasing the dependence level of claim sizes the ruin probability of the risk process increases, while its time to ruin decreases

In this paper, three new non-parametric estimator for upper tail dependence measure are introduced and it is shown that these estimators are consistent and asymptotically unbiased. Also these estimators are compared using the Mont Carlo simulation of three different copulas and present a new method in order to select the best estimator by applying the real data.

One of the typical aims of statistical shape analysis, in addition to deriving an estimate of mean shape, is to get an estimate of shape variability. This aim is achived through employing the principal component analysis. Because the principal component analysis is limited to data on Euclidean space, this method cannot be applied for the shape data which are inherently non-Euclidean data. In this situation, the principal geodesic analysis or its linear approximation can be used as a generalization of the principal component analysis in non-Euclidean space. Because the main root of this method is the gradient descent algorithm, revealing some of its main defects, a new algorithm is proposed in this paper which leads to a robust estimate of mean shape and also preserves the geometrical structure of shape. Then, providing some theoretical aspects of principal geodesic analysis, its application is evaluated in a simulation study and in real data.

In a sequence of multivariate random variables, when the experimenter is interested in ordering one of the variables, the corresponding ordered random variables are referred to as concomitants. In this paper, the distribution properties of the bivariate concomitants of record values and order statistics are first studied. Then, by considering the trivariate pseudo exponential family, the amount of Fisher information contained in these random variables is investigated.

On Hypergeometric Generalized Negative Binomial Distribution in Promotion Time Cure Model In analysis of survival data if exposes a high percentage of censoring due to termination of the study, whereas the study has lasted long enough, it is preferred to utilize cure models. These models, which are based on the latent variable distribution, has obtained much attention in the last decade. In this paper the Hypergeometric Generalized Negative Binomial distribution of the latent variable is used to model the long time survival data. The new model parameters are estimated in Bayesian approach. This model is applied for a Primary Biliary Cirrhosis clinical trial data and a simulated data set. With respect to DIC, Hypergeometric Generalized Negative Binomial model is a suitable fit to the data.

Suppose there are two groups of random variables, one with independent and non-identical distributed and another with independent and identical distributed. In this paper, for the case when the size of groups are not equal, and all of the underlying random variables have exponential distribution, the necessary and sufficient conditions are obtained for establishing the mean residual life, hazard rate and dispersive orders between the second order statistics of two groups. Moreover, when random variables follow the Weibull distribution, the hazard rate, dispersive and likelihood ratio order between the second order statistics from two groups are investigated.

In some semiparametric survival models with time dependent coefficients, a closed-form solution for coefficients estimates does not exist. Therefore, they have to be estimated by using approximate numerical methods. Due to the complicated forms of such estimators, it is too hard to extract their sampling distributions. In such cases, one usually uses the asymptotic theory to evaluate properties of the estimators. In this paper, first the model is introduced and a method is proposed, by using the Taylor expansion and kernel methods, to estimate the model. Then, the consistency and asymptotic normality of the estimators are established. The performance of the model and estimating procedure are evaluated by a heavy simulation study as well. Finally, the proposed model is applied on a real data set on heart disease patients in one of the Mashhad hospitals.

In this paper, two new entropy estimators are proposed. Then, entropy-based tests of exponentiality based on our entropy estimators are introduced. Simulation results show that the proposed estimators and related goodness of fit tests have good performances in comparison with their leading competitors.

In this  paper  the  regression analysis with finite mixture bivariate poisson response variable is investigated from the Bayesian point of view. It is shown that  the posterior distribution can not be written in a closed form due to the  complexity of the likelihood function of bivariate Poisson distribution. Hence, the full conditional posterior distributions of the parameters are computed and the Gibbs algorithm is used to sampling from posterior distributions. A simulation study is performed in order to assess the proposed Bayesian model and its efficiency in estimation of the parameters is compared with their frequentist counterparts. Also, a real example presented to illustrate and assess the proposed Bayesian model. The results indicate to the more efficiency of the  estimators resulted from Bayesian  approach than estimators of frequentist approach at least for small sample sizes.

Although the measurement error exists in the most scientific experiments, in order to simplify the modeling, its presence is usually ignored in statistical studying. In this paper, various approaches on estimating the parameters of multilevel models in presence of measurement error are studied. In addition, to improve the parameter estimates in this case, a new method is proposed which has high precision and reasonable convergence rate in compare with previous common approaches. Also, the performance of the proposed method as well as usual approaches are evaluated and compared using simulation study and analyzing real data of the income-expenditure of some households in Tehran city in 2008.

In this paper the likelihood and Bayesian inference of the stress-strength reliability are considered based on record values from proportional and proportional reversed hazard rate models. Then inference of the stress-strength reliability based on lower record values from some generalized distributions are also considered. Next the likelihood and Bayesian inference of the stress-strength model based on upper record values from Gompertz, Burr type XII, Lomax and Weibull distributions are considered. The ML estimators and their properties are studied. Likelihood-based confidence intervals, exact, as well as the Bayesian credible sets and bootstrap interval for the stress-strength reliability in all distributions are obtained. Simulation studies are conducted to investigate and compare the performance of the intervals.

In this paper, first the Bhattacharray and Kshirsagar bounds are introduced and then the multiparameter Bhattacharyya bound is presented in simpler and understandable form. Furthermore, the multiparameter Kshirsagar lower bound, which has not been studied yet, is obtained. Finally, by presenting some example of Log-normal distribution, the bounds are computed and compared.

In this paper, some various families constructed from the logit of the generalized Beta, Beta, Kumar, generalized Gamma, Gamma, Weibull, log gamma and Logistic distributions are reviewed. Then a general family of distributions generated from the logit of the normal distribution is proposed. A special case of this family, Normal-Uniform distribution, is defined and studied. Various properties of the distribution are also explored. The maximum likelihood and minimum spacings estimators of the parameters of this distribution are obtained. Finally, the new distribution is effectively used to analysis a real survival data set.

In this paper we consider of location parameter estimation in the multivariate normal distribution with unknown covariance. Two restrictions on the mean vector parameter are imposed. First we assume that all elements of mean vector are nonnegative, at the second hand assumed only a subset of elements are nonnegative. We propose a class of shrinkage estimators which dominate the minimax estimator of mean vector under the quadratic loss function.

In this paper, we deal with modeling crisp input-fuzzy output data by constructing a MARS-fuzzy regression model with crisp parameters estimation and fuzzy error terms for the fuzzy data set. The proposed method is a two-phase procedure which applies the MARS technique at phase one and an optimization problem at phase two to estimate the center and fuzziness of the response variable. A realistic application of the proposed method is also presented in a hydrology engineering problem. Empirical results demonstrate that the proposed approach is more efficient and more realistic than some traditional least-squares fuzzy regression models.