Journal of Statistical Research of Iran
Volume:7 Issue: 1, 2011

Using the concept of system signature introduced by Samaniego (1985), Kochar et al. (1999) compared the lifetimes of the systems in which the lifetimes of the components are independent and identically distributed (i.i.d.) random variables. Their results are extended to the systems with exchangeable components by Navarro et al. (2005). This paper gives some alternative proofs to obtain their results. Particularly in view of the hazard rate ordering, we compare two systems with different structures and components, which extends Theorem 8 in Navarro et al. (2005). We also compare two systems with different structures and components in view of the likelihood ratio ordering. Some illustrative examples are mentioned.

In this paper, we obtain the distribution functions of the range and the quasi-range of the random variables arising from the extended type I generalized logistic distribution.

One of the new area of research emerging in the field of statistics is the shape analysis. Shape is defined as all the geometrical information of an object whose location, scale and orientation is not of interest. Diffusion in shape analysis can be studied via either perturbation of the key coordinates identifying the initial object or random evolution of the shape itself. Reviewing the first case, we mainly consider the second case and particularly define a new family of diffusion processes. It can be used to model diffusion phenomena represented by shape evolution such as cell motion.

The mixture of Type I and Type II censoring schemes, called the hybrid censoring. This article presents the statistical inferences on lognormal parameters when the data are hybrid censored. We obtain the maximum likelihood estimators (MLEs) and the approximate maximum likelihood estimators (AMLEs) of the unknown parameters. Asymptotic distributions of the maximum likelihood estimators are used to construct approximate confidence intervals. Monte Carlo simulations are performed to compare the performances of the different methods and one data set is analyzed for illustrative purposes.

In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, -Divergence, … and so on. Properties and results related to distance between probability distributions derived via copula functions. Some inequalities are obtained in view of the dependence and information measures.

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC(λ1, λ2), that it has more flexible than the skew-Cauchy distribution (denoted by SC(λ)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC(λ1, λ2) can fits the data better than SC(λ).

We consider the problem of estimating the scale parameter β of a rescaled F-distribution when β has a lower bounded constraint of the form β≥a, under the entropy loss function. An admissible minimax estimator of the scale parameter β, which is the pointwise limit of a sequence of Bayes estimators, is given. Also in the class of truncated linear estimators, the admissible estimators and the only minimax estimator of β are obtained.