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Debasis Kundu - One of the best experts on this subject based on the ideXlab platform.
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multivariate geometric skew Normal Distribution
Statistics, 2017Co-Authors: Debasis KunduAbstract:ABSTRACTAzzalini [A class of Distributions which include the Normal. Scand J Stat. 1985;12:171–178] introduced a skew-Normal Distribution of which Normal Distribution is a special case. Recently, Kundu [Geometric skew Normal Distribution. Sankhya Ser B. 2014;76:167–189] introduced a geometric skew-Normal Distribution and showed that it has certain advantages over Azzalini's skew-Normal Distribution. In this paper we discuss about the multivariate geometric skew-Normal (MGSN) Distribution. It can be used as an alternative to Azzalini's skew-Normal Distribution. We discuss different properties of the proposed Distribution. It is observed that the joint probability density function of the MGSN Distribution can take a variety of shapes. Several characterization results have been established. Generation from an MGSN Distribution is quite simple, hence the simulation experiments can be performed quite easily. The maximum likelihood estimators of the unknown parameters can be obtained quite conveniently using th...
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multivariate geometric skew Normal Distribution
arXiv: Methodology, 2017Co-Authors: Debasis KunduAbstract:Azzalini (1985) introduced a skew-Normal Distribution of which Normal Distribution is a special case. Recently Kundu (2014) introduced a geometric skew-Normal Distribution and showed that it has certain advantages over Azzalini's skew-Normal Distribution. In this paper we discuss about the multivariate geometric skew-Normal Distribution. It can be used as an alternative to Azzalini's skew Normal Distribution. We discuss different properties of the proposed Distribution. It is observed that the joint probability density function of the multivariate geometric skew Normal Distribution can take variety of shapes. Several characterization results have been established. Generation from a multivariate geometric skew Normal Distribution is quite simple, hence the simulation experiments can be performed quite easily. The maximum likelihood estimators of the unknown parameters can be obtained quite conveniently using expectation maximization (EM) algorithm. We perform some simulation experiments and it is observed that the performances of the proposed EM algorithm are quite satisfactory. Further, the analyses of two data sets have been performed, and it is observed that the proposed methods and the model work very well.
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bivariate sinh Normal Distribution and a related model
Brazilian Journal of Probability and Statistics, 2015Co-Authors: Debasis KunduAbstract:Sinh-Normal Distribution is a symmetric Distribution with three parameters. In this paper we introduce bivariate sinh-Normal Distribution, which has seven parameters. Due to presence of seven parameters it is a very flexible Distribution. Different properties of this new Distribution has been established. The model can be obtained as a bivariate Gaussian copula also. Therefore, using the Gaussian copula property, several properties of this proposed Distribution can be obtained. Maximum likelihood estimators cannot be obtained in closed forms. We propose to use two step estimators based on Copula, which can be obtained in a more convenient manner. One data analysis has been performed to see how the proposed model can be used in practice. Finally, we consider a bivariate model which can be obtained by transforming the sinh-Normal Distribution and it is a generalization of the bivariate Birnbaum-Saunders Distribution. Several properties of the bivariate Birnbaum-Saunders Distribution can be obtained as special cases of the proposed generalized bivariate Birnbaum-Saunders Distribution. AMS Subject Classification: Primary 62E15, Secondary 62H10.
Hong Zhao - One of the best experts on this subject based on the ideXlab platform.
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test cost sensitive attribute reduction of data with Normal Distribution measurement errors
Mathematical Problems in Engineering, 2013Co-Authors: Hong ZhaoAbstract:The measurement error with Normal Distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making, we will select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform Distribution error was proposed to investigate this issue. However, the measurement errors satisfy Normal Distribution instead of uniform Distribution which is rather simple for most applications. In this paper, we introduce Normal Distribution measurement errors to covering-based rough set model and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are fourfold. First, we build a new data model based on Normal Distribution measurement errors. Second, the covering-based rough set model with measurement errors is constructed through the “3-sigma” rule of Normal Distribution. With this model, coverings are constructed from data rather than assigned by users. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The experimental results show that the algorithm is more effective and efficient than the existing one. This study suggests new research trends concerning cost-sensitive learning.
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test cost sensitive attribute reduction of data with Normal Distribution measurement errors
arXiv: Artificial Intelligence, 2012Co-Authors: Hong ZhaoAbstract:The measurement error with Normal Distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform Distribution error was proposed to investigate this issue. However, the measurement errors satisfy Normal Distribution instead of uniform Distribution which is rather simple for most applications. In this paper, we introduce Normal Distribution measurement errors to covering-based rough set model, and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are four-fold. First, we build a new data model based on Normal Distribution measurement errors. With the new data model, the error range is an ellipse in a two-dimension space. Second, the covering-based rough set with Normal Distribution measurement errors is constructed through the "3-sigma" rule. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The algorithm is tested on ten UCI (University of California - Irvine) datasets. The experimental results show that the algorithm is more effective and efficient than the existing one. This study is a step toward realistic applications of cost-sensitive learning.
Barry C. Arnold - One of the best experts on this subject based on the ideXlab platform.
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a doubly skewed Normal Distribution
Statistics, 2015Co-Authors: Barry C. Arnold, Hector W Gomez, Hugo S SalinasAbstract:We consider a Distribution obtained by combining two well-known mechanisms for generating skewed Distributions. In this manner we arrive at a flexible model which subsumes and extends several skew Distributions which have been discussed in the literature. One approach to the problem of generating skewed Distributions was first popularized by Azzalini [A class of Distributions which includes the Normal ones. Scand J Stat. 1985;12:171–178]. The single constraint skew Normal Distribution that was studied by Azzalini is of the form fSN(x)=2φ(x)Φ(αx), where φ and Φ denote, respectively, the standard Normal density and Distribution function and α∈ℝ is a skewing parameter. Multiple constraint variations of this Distribution have also been considered. The second skewing approach that we will consider was proposed by Mudholkar and Hutson [The epsilon-skew-Normal Distribution for analyzing near-Normal data. J Statist Plann Inference. 2000;83:291–309] and called an epsilon-skew-Normal Distribution. The combination o...
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a conditional characterization of the multivariate Normal Distribution
Statistics & Probability Letters, 1994Co-Authors: Barry C. Arnold, Enrique Castillo, Jose Maria SarabiaAbstract:If X is a k-dimensional random vector, we denote by X(i,j) the vector X with coordinates i and j deleted. If for each i, j the conditional Distribution of Xi, Xj given X(i,j) = x(i,j) is classical bivariate Normal for each then it is shown that X has a classical k-variate Normal Distribution.
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the nontruncated marginal of a truncated bivariate Normal Distribution
Psychometrika, 1993Co-Authors: Barry C. Arnold, Richard A Groeneveld, Robert J Beaver, William Q. MeekerAbstract:Inference is considered for the marginal Distribution ofX, when (X, Y) has a truncated bivariate Normal Distribution. TheY variable is truncated, but only theX values are observed. The relationship of this Distribution to Azzalini's “skew-Normal” Distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini Distribution. Samples that are uniformative about the skewness of this Distribution may occur, even for largen. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.
A Van Den Bos - One of the best experts on this subject based on the ideXlab platform.
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the multivariate complex Normal Distribution a generalization
IEEE Transactions on Information Theory, 1995Co-Authors: A Van Den BosAbstract:The multivariate complex Normal Distribution usually employed in the literature is a special case since certain restrictions have been imposed on the covariances of the real and imaginary parts of its variables. A more general Distribution is proposed of which the usual Distribution is shown to be a special case. >
Boris Iglewicz - One of the best experts on this subject based on the ideXlab platform.
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on singular multivariate Normal Distribution and its applications
Computational Statistics & Data Analysis, 1996Co-Authors: Koonshing Kwong, Boris IglewiczAbstract:Abstract The methods of evaluating the singular multivariate Normal Distribution have been commonly applied even though the complete analytical proofs are not found. Recently, those evaluation methods are shown to have some errors. In this paper we present a new approach with a complete proof for evaluating the exact two-sided percentage points of a standardized m -variate Normal Distribution with a singular negative product correlation structure for m = 3 and with a singular negative equi-correlated structure for m ⩾ 3. The results are then applied to modify the existing procedures for estimating joint confidence intervals for multinomial proportions and for determining sample sizes. By extending the results from the multivariate Normal Distribution to the multivariate t -Distribution with the corresponding singular correlation structure, we obtain the corrected two-sided exact critical values for the Analysis of Means for m = 4,5.
