Journal of Statistical Research of Iran
Volume:1 Issue: 1, 2004

Let a0(ω), a1(ω), a2(ω),. .., an(ω) be a sequence of independent random variables defined on a fixed probability space (Ω,Pr, A). There are many known results for the expected number of real zeros of a polynomial a0(ω)ψ0(x) + a1(ω)ψ1(x) + a2(ω)ψ2(x) +. .. + an(ω)ψn(x) where ψj(x), j = 0, 1, 2,. .., n is a specific function of x. In this paper we highlight different characteristics arising for the random polynomial dictated by assuming different values for ψj(x). Then we are able to classify random polynomials into three classes each of which share common properties. Although, we are mainly concerned with the number of real roots we also study the density of complex roots generated by assuming complex random coefficients for polynomials.

Many Limit Theorems, Convergence Theorems and Characterization Theorems in Probability and Statistics, in particular those related to normal distribution, are based on the assumption of independence of two or more random variables.However, the full power of independence is not used in the proofs of these Theorems, since it is the distribution of summation of the random variables which is needed and not the joint distribution of the variables. A concept is re-introduced, which is quite weak in comparison to independence, and can replace the concept of independence in most of the above mentioned theorems. Another relatively new concept will also be mentioned and some related results are discussed.

Traditional regression analyses assume normality of observations and independence of mean and variance. However, there are many examples in science and Technology where the observations come from a skewed distribution and moreover there is a functional dependence between variance and mean.In this article, we propose a method for regression analysis under Inverse Gaussian model when there are repeated observations for a fixed value of explanatory variable. The problem is treated by likelihood, Bayes, and empirical Bayes procedures, using conjugate priors. Inferences are provided for regression analysis.© Statistical Research and Training Center. All rights reserved.

About 25 years ago, McCullagh proposed a method for modeling univariate ordinal responses. After publishing this paper, other statisticians gradually extended his method, such that we are now able to use more complicated but efficient methods to analyze correlated multivariate ordinal data, and model the relationship between these responses and host of covariates. In this paper, we aim to present the recent progressions in modeling ordinal response data, especially in bivariate ordinal responses that arise from medical studies relating to paired organs such as ophthalmology, otology, nephrology etc. Additionally, we present a new model for analyzing correlated ordinal response data. This model is an appropriate alternative for bivariate cumulative probit regression model, when joint distribution of response data is not symmetric. Finally, as an applied example, we analyze the obtained data from an epidemiologic study relating to periodontal status among high school students in Tehran using this method and compare the results with the similar models.

The existence and non-existence of trend-resistant repeated measurement designs are investigated. Two families of efficient/optimal repeated measurement designs which are very popular among experimenters are shown to be trend-resistant or trend-resistant with respect to treatments.

In this paper an applied problem, where the response of interest is the number of success in a specific experiment, is considered and by various visions is studied. The effects of outlier values of response on results of a regression analysis are so important to be studied. For this reason, using diagnostic methods, outlier response values are recognized. It is shown that use of arc-sine transformation many be misleading in recognizing response outliers. If deleting of outliers is not possible, use of robust modeling approach is suggested. Method of maximum likelihood for estimating parameters in generalized linear model, transformation method and also pseudo-likelihood method are not robust. A method, which is called robust pseudo-likelihood and leads to robust results, is reviewed and a simpler method of computing P-values for model selection is presented. Various approaches for modeling are also compared in the applied example.