The exponentiated half logistic (EHL) distribution can be mostly and effectively used in modeling lifetime data. It is very similar to the gamma and exponentiated exponential distributions with two parameters. The maj...
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The exponentiated half logistic (EHL) distribution can be mostly and effectively used in modeling lifetime data. It is very similar to the gamma and exponentiated exponential distributions with two parameters. The major advantage of EHL distribution over the gamma distribution is that its cumulative distribution has a closed form. In this research, we develop a new bivariate exponentiated half logistic (BEHL) distribution with univariate EHL distribution as the marginals. The joint probabilitydensityfunction and the joint cumulative distribution function were expressed in explicit forms. This article also presents the various properties of the proposed distribution such as marginal, conditional distributions and product moments. The maximum likelihood estimates for the unknown parameters of BEHL distribution and their approximate variance- covariance matrix have been obtained. Monte Carlo simulations have been conducted to check the performances of the maximum likelihood estimators with applications to a real data set. Analysis showed that the BEHL distribution gives a better fit than other rival bivariate probability models.
When the characteristics of non-Gaussian time series such as biological signals are described, not only power spectra but also higher-order spectra are required. In order to obtain estimated values with few statistica...
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When the characteristics of non-Gaussian time series such as biological signals are described, not only power spectra but also higher-order spectra are required. In order to obtain estimated values with few statistical fluctuations, some parametric estimation method has to be established. As the parametric model, regression-function-based autoregressive models Such as the neural network autoregressive model have been Studied so far. On the other hand, probability-density-based autoregressive models in which the correlation information of the time series is represented by the conditional probability density function have been proposed. However, in the existing probability-density-based autoregressive models, higher-order spectral estimation is not assumed. So, if we adopt the probability-density-based autoregressive model for the estimation of higher-order spectra, some problems such as the stationarity arise. In this paper, we proposed a new probability-density-based autoregressive model using the support vector method. Further, we estimated higher-order spectra of the time series by the proposed model. (C) 2006 Wiley Periodicals, Inc.
The evolution of the 4-variate probability distribution of the diameter at the breast height, total height, crown base height, and crown width against the age in a forest stand is of great interest to forest managemen...
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The evolution of the 4-variate probability distribution of the diameter at the breast height, total height, crown base height, and crown width against the age in a forest stand is of great interest to forest management and the evaluation of forest resources. This paper focuses on the Vasicek type 4-variate fixed effect stochastic differential equation (SDE) to quantify the dynamic of tree size components distribution against the age. The new derived 4-variate probabilitydensityfunction and its marginal univariate, bivariate, trivariate, and conditional univariate distributions are applied for the modeling of stand attributes such as the mean diameter, height, crown base height, crown width, volume, and slenderness. All parameters were estimated by the maximum likelihood procedure using a dataset of 1630 Scots pine trees (12 stands). The results were validated using a dataset of 699 Scots pine trees (five stands). A newly developed 4-variate simultaneous system of SDEs incorporated covariance structure driving changes in tree size components and improved predictions in one tree size component given the other tree size components in the system.
Closed-form solutions are analytically derived for stochastic properties of earthquake ground motion fields, which are conditioned by an observed time series at certain observation sites and are characterized by spect...
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Closed-form solutions are analytically derived for stochastic properties of earthquake ground motion fields, which are conditioned by an observed time series at certain observation sites and are characterized by spectra with uncertainties. The theoretical framework presented here can estimate not only the expectations of such simulated earthquake ground motions, but also the prediction errors which offer important information for the field of engineering. Before these derivations are made, the theory of conditional random fields is summarized for convenience in this study. Furthermore, a method for stochastic interpolation of power spectra is explained.
Recently, Gupta and Kundu [R.D. Gupta and D. Kundu, A new class of weighted exponential distributions, Statistics 43 (2009), pp. 621-634] have introduced a new class of weighted exponential (WE) distributions, and thi...
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Recently, Gupta and Kundu [R.D. Gupta and D. Kundu, A new class of weighted exponential distributions, Statistics 43 (2009), pp. 621-634] have introduced a new class of weighted exponential (WE) distributions, and this can be used quite effectively to model lifetime data. In this paper, we introduce a new class of weighted Marshall-Olkin bivariate exponential distributions. This new singular distribution has univariate WE marginals. We study different properties of the proposed model. There are four parameters in this model and the maximum-likelihood estimators (MLEs) of the unknown parameters cannot be obtained in explicit forms. We need to solve a four-dimensional optimization problem to compute the MLEs. One data set has been analysed for illustrative purposes and finally we propose some generalization of the proposed model.
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