Journal of Statistical Sciences

Analyzing the Estimators of Upper Tail Dependence Measure

Mahla Ghasemnejad Farsangi

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.

Stochastic Comparisons Between Sample Spacings of Order Statistics from Independent Exponential Random Variables

Ghobad Barmalzan

Suppose there are two groups of independent exponential random variables, where the first group has different hazard rates and the second group has common hazard rate. In this paper, the various stochastic orderings between their sample spacings have studied and introduced some necessary and sufficient conditions to equivalence of these stochastic ordering. Also, for the special case of sample size two, it is shown that the hazard rate function of the second sample spacing is Shcur-concave in the inverse vector of parameters.

Adaptive Progressive Type-I Censoring and its Applications in Life Testing

Mohamad Bayat

Nowadays, the use of various types of censoring plan in studies of lifetime engineering systems and industrial experiment are worthwhile. In this paper, by using the idea in Cramer and Iliopoulos (2010), an adaptive progressive Type-I censoring is introduced. It is assumed that the next censoring number is random variable and depends on the previous censoring numbers, previous failure times and censoring times. General distributional results are obtained in explicit analytic forms. It is shown that maximum likelihood estimators coincide with those in deterministic progressive Type-I censoring. Finally, in order to illustrate and make a comparison, simulation study is done for one-parameter exponential distribution.

Fisher Information in Bivariate Concomitants of Record Values and Order Statistics in Pseudo Exponential Model

Samaneh Jalambadanis

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.

A Multivariate Bayesian Model for Gene Networks

Hamid Pezeshk

There are several methods for inference about gene networks, but there are few cases in which the historical information have been considered. In this research we deal with Bayesian inference on gene network. We apply a Bayesian framework to use the available information. Assuming a proper prior distribution and taking the dependency of parameters into account, we seek a model to obtain promising results. We also deal with the hyper parameter estimation. Two methods are considered. The results will be compared by the use of a simulation based on Gibbs sampler. The strengths and weaknesses of each method are briefly mentioned.

Bayes Estimation of the Parameter of Pareto Distribution Under Squared Error and LINEX Loss Functions Based on Ranked Set Sampling

Reza Alizadeh Noughabi

In some practical problems, obtaining observations for the variable of interest is costly and time consuming. In such situations, considering appropriate sampling schemes, in order to reduce the cost and increase the efficiency are worthwhile. In these cases, ranked set sampling is a suitable alternative for simple random sampling. In this paper, the problem of Bayes estimation of the parameter of Pareto distribution under squared error and LINEX loss functions is studied. Using a Monte Carlo simulation, for both sampling methods, namely, simple random sampling and ranked set sampling, the Bayes risk estimators are computed and compared. Finally, the efficiency of the obtained estimators is illustrated throughout using a real data set. The results demonstrate the superiority of the ranked set sampling scheme, therefore, we recommend using ranked set sampling method whenever possible.

Improving Performance of the Principal Geodesic Analysis in Statistical Shape Analysis

Mousa Golalizadeh

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.