Journal of Iranian Statistical Society
Volume:13 Issue: 1, 2014

The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS''s as well as two sub-vectors of $p$-spacings based on two continuous distribution functions. In particular, we apply the new results to obtain some computable bounds on the mean residual life of some unobserved progressive type II censored order statistics.

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function $F$, within this set of observations denote the random number of records by $M$. This is called geometric random record model. In this paper, characterizations of $F$ are provided in terms of the subsequences entropies of records conditional on events ${M geq n}$ or ${M = n}$ in a geometric random record model. Characterization results for symmetric distributions are also presented based on entropies of upper and lower records in a random record model.

One of the main problems in credit risk management is the correlated default. In large portfolios, computing the default dependencies among issuers is an essential part in quantifying the portfolio''s credit. The most important problems related to credit risk management are understanding the complex dependence structure of the associated variables and lacking the data. This paper aims at introducing a new methodology for credit risk management based on Bayesian copulas. In this paper, the focus is specifically on a new method of simulating the joint distribution of default risk. This methodology joins the use of copulas and Bayesian models. Using copulas, the joint multivariate probability distribution of a random vector can be separated into individual components characterized by marginal distributions. The model is based on a jump diffusion process for the intensities. Another important problem in credit risk management is the lack of data, which influences the parameter estimation. Considering this drawback, the employment of Bayesian methods and simulation tools could be a natural solution to the problem. This suggests the use of Bayesian models, computed via simulation methods and in particular, Markov chain Monte Carlo. Bayesian methods in Student''s $t$ copula are efficient enough for heavy tail distribution. Moreover, our main outcome is that the application of Bayesian methodology causes a reduction of measure while that copula is Student''s $t$. Finally, the conclusion of Bayesian copulas with classic copulas was compared through a simulation study.

Generalized variance is applied for determination of dispersion in a multivariate population and is a successful measure for concentration of multivariate data. In this article, we consider constructing confidence interval and testing the hypotheses about generalized variance in a multivariate normal distribution and give a computational approach. Simulation studies are performed to compare this approach and three approximate methods; the simulations show that our approach is satisfactory. At the end, two practical examples are given.

In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the nth moment, the median, the mode and the 100k-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of computer program and a theorem that relate the generalized distribution to Pareto distribution was stated and proved. Finally, we obtained the distributions of some order statistics from the generalized half logistic distribution.

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.