Journal of Iranian Statistical Society
Volume:18 Issue: 2, 2019

Goodness-of-fit tests are constructed for the two-parameter Birnbaum-Saunders distribution in the case where the parameters are unknown and therefore are estimated from the data. In each test, the procedure starts by computing efficient estimators of the parameters. Then the data are transformed by a normal transformation and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Three classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function and the final class utilizes the Kullback-Leibler information function. All methods are extended to cover the case of generalized three-parameter Birnbaum-Saunders distributions.

In this paper, the kernel distribution function estimator for negative superadditive dependent (NSD) random variables is studied. The exponential inequalities and exponential rate for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth is determined using the mean squared error and is found to be the same as that in the independent identically distributed case. A simulation study to examine the behavior of the kernel and empirical estimators is given. Moreover, a real data set in hydrology is analyzed to demonstrate the structure of negative superadditive dependence, and as a result, the kernel distribution function estimator of the data is investigated.

Testing exponentiality has long been an interesting issue in statistical inferences. The present article is based on a modified measure of distance between two distributions. The proposed new measure is similar to the Kullback-Leibler divergence and it is related to the Lin-Wong divergence applied on the residual lifetime data. A modified measure is developed here which is a consistent test statistic for testing the hypothesis of exponentiality against some alternatives. First, we consider a method similar to Vasicek's and Correa's techniques of estimating the density function in order to construct statistic for LW divergence. Then the critical values of the test are computed, using a Monte-Carlo simulation method. Also, we find the differences of exponential distribution detection power between the proposed test and other tests. It is shown that the proposed test performs better than other tests of exponentiality when the hazard rate is in the form of an increasing function. Finally, a case of application of the proposed test is shown through two illustrative examples.

This paper develops a new class of spatio-temporal process models that can simultaneously capture skewness and non-stationarity. The proposed approach which is based on using the closed skew-normal distribution in the low-rank representation of stochastic processes, has several favorable properties. In particular, it greatly reduces the dimension of the spatio-temporal latent variables and induces flexible correlation structures. Bayesian analysis of the model is implemented through a Gibbs MCMC algorithm which incorporates a version of the Kalman filtering algorithm. All fully conditional posterior distributions have closed forms which show another advantageous property of the proposed model. We demonstrate the efficiency of our model through an extensive simulation study and an application to a real data set comprised of precipitation measurements.

This paper presents a skew-normal mean-variance mixture based on Birnbaum-Saunders (SNMVBS) distribution and discusses some of its key properties. The SNMVBS distribution can be thought as a flexible extension of the normal mean-variance mixture based on Birnbaum-Saunders (NMVBS) distribution as it possesses one additional shape parameter for providing more flexibility with skewness and kurtosis. Next, we develop a computationally feasible ECM algorithm for the maximum likelihood estimation of the model parameters. Asymptotic standard errors of the ML estimates are obtained through an approximation of the observed information matrix. Finally, the usefulness of the proposed model and its fitting method are illustrated through a Monte-Carlo simulation as well as three real-life datasets.

This paper introduces a functional mixed effect random model to model spatial data. In this model, the spatial locations form the index set, while the contributing effects to the response variable are set as a linear mixture of fixed and random effects. These fixed and random effects are linear combinations of L2 functions and random elements, respectively. However, the corresponding linear factors depend on the spatial location variable. Therefore, we develop estimation procedures to estimate the fixed and random coefficients, using spatial functional principal component analysis. Then, we perform prediction by adapting the functional universal kriging method to our model.

We propose a copula-based index to detect the reflection asymmetry in trivariate distributions. The proposed index is based on the definition of directional reflection asymmetry over the set of directions. We derive the asymptotic distribution of the rank-based estimator of the proposed index. The value of the index and the direction in which the asymmetry occurs are easily computed, and we illustrate it with a simulation study and a real data analysis.

This article addresses the problem of Bayesian shrinkage estimation for the Rayleigh scale parameter based on record values under the reflected gamma loss (RGL) function. A class of Bayesian shrinkage estimators using prior point information is constructed. The risk functions of the maximum likelihood estimator (MLE) and proposed Bayesian shrinkage estimator are derived under the RGL function. The performance of Bayesian shrinkage estimator is compared with the MLE numerically and graphically. One data set has been analyzed to illustrate the performance of the Bayesian shrinkage estimator.

In the present article, we develop the well-known preliminary test and Stein-type estimators for the probability density function under association. In this respect, we derive the asymptotic characteristics of the proposed estimators under a set of local alternatives. Some numerical studies are provided for supporting the findings. The result of this article improves the kernel estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. For practical sake, the behavior of the proposed estimators is also analyzed using a real data set.

In this article, the tests on parallelism, equal intercept and sets of lines intersected at a fixed value for a set of r simple linear models or a set of r linearizable regression models are generalized to the multivariate case, r = 2, 3,..., R. Likewise, the normality hypothesis is replaced assuming an elliptical matrix variate distribution, concluding that the tests obtained under normality are valid and are invariant under the whole family of elliptical matrix variate distributions. Finally, an application in an agricultural acarology context is provided.