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Debasis Kundu - One of the best experts on this subject based on the ideXlab platform.

  • Bivariate discrete generalized exponential distribution
    Statistics, 2017
    Co-Authors: Vahid Nekoukhou, Debasis Kundu
    Abstract:

    ABSTRACTIn this paper, we develop a Bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram [Discrete generalized exponential distribution of a second type. Statistics. 2013;47:876–887]. It is observed that the proposed Bivariate distribution is a very flexible distribution and the Bivariate geometric distribution can be obtained as a special case of this distribution. The proposed distribution can be seen as a natural discrete analogue of the Bivariate generalized exponential distribution proposed by Kundu and Gupta [Bivariate generalized exponential distribution. J Multivariate Anal. 2009;100:581–593]. We study different properties of this distribution and explore its dependence structures. We propose a new EM algorithm to compute the maximum-likelihood estimators of the unknown parameters which can be implemented very efficiently, and discuss some inferential issues also. The analysis of on...

  • Bivariate discrete generalized exponential distribution
    arXiv: Methodology, 2017
    Co-Authors: Vahid Nekoukhou, Debasis Kundu
    Abstract:

    In this paper we develop a Bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram ("Discrete generalized exponential distribution of a second type", Statistics, 47, 876 - 887, 2013). It is observed that the proposed Bivariate distribution is a very flexible distribution and the Bivariate geometric distribution can be obtained as a special case of this distribution. The proposed distribution can be seen as a natural discrete analogue of the Bivariate generalized exponential distribution proposed by Kundu and Gupta ("Bivariate generalized exponential distribution", Journal of Multivariate Analysis, 100, 581 - 593, 2009). We study different properties of this distribution and explore its dependence structures. We propose a new EM algorithm to compute the maximum likelihood estimators of the unknown parameters which can be implemented very efficiently, and discuss some inferential issues also. The analysis of one data set has been performed to show the effectiveness of the proposed model. Finally we propose some open problems and conclude the paper.

  • Bivariate sinh normal distribution and a related model
    Brazilian Journal of Probability and Statistics, 2015
    Co-Authors: Debasis Kundu
    Abstract:

    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.

  • modified sarhan balakrishnan singular Bivariate distribution
    Journal of Statistical Planning and Inference, 2010
    Co-Authors: Debasis Kundu, Rameshwar D Gupta
    Abstract:

    Abstract Recently Sarhan and Balakrishnan [2007. A new class of Bivariate distribution and its mixture. Journal of Multivariate Analysis 98, 1508–1527] introduced a new Bivariate distribution using generalized exponential and exponential distributions. They discussed several interesting properties of this new distribution. Unfortunately, they did not discuss any estimation procedure of the unknown parameters. In this paper using the similar idea as of Sarhan and Balakrishnan [2007. A new class of Bivariate distribution and its mixture. Journal of Multivariate Analysis 98, 1508–1527], we have proposed a singular Bivariate distribution, which has an extra shape parameter. It is observed that the marginal distributions of the proposed Bivariate distribution are more flexible than the corresponding marginal distributions of the Marshall–Olkin Bivariate exponential distribution, Sarhan–Balakrishnan's Bivariate distribution or the Bivariate generalized exponential distribution. Different properties of this new distribution have been discussed. We provide the maximum likelihood estimators of the unknown parameters using EM algorithm. We reported some simulation results and performed two data analysis for illustrative purposes. Finally we propose some generalizations of this Bivariate model.

  • Estimating the parameters of the Marshall-Olkin Bivariate Weibull distribution by EM algorithm
    Computational Statistics & Data Analysis, 2009
    Co-Authors: Debasis Kundu, Arabin Kumar Dey
    Abstract:

    In this paper we consider the Marshall-Olkin Bivariate Weibull distribution. The Marshall-Olkin Bivariate Weibull distribution is a singular distribution, whose both the marginals are univariate Weibull distributions. This is a generalization of the Marshall-Olkin Bivariate exponential distribution. The cumulative joint distribution of the Marshall-Olkin Bivariate Weibull distribution is a mixture of an absolute continuous distribution function and a singular distribution function. This distribution has four unknown parameters and it is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. In this paper we discuss about the computation of the maximum likelihood estimators of the unknown parameters using EM algorithm. We perform some simulations to see the performances of the EM algorithm and re-analyze one data set for illustrative purpose.

N Balakrishnan - One of the best experts on this subject based on the ideXlab platform.

  • a robust multivariate birnbaum saunders distribution em estimation
    Statistics, 2018
    Co-Authors: Renata G. Romeiro, Filidor Vilca, N Balakrishnan
    Abstract:

    We propose here a robust multivariate extension of the Bivariate Birnbaum–Saunders (BS) distribution derived by Kundu et al. [Bivariate Birnbaum–Saunders distribution and associated inference. J Mu...

  • Bivariate conway maxwell poisson distribution
    Journal of Multivariate Analysis, 2016
    Co-Authors: Kimberly F Sellers, Darcy Steeg Morris, N Balakrishnan
    Abstract:

    The Bivariate Poisson distribution is a popular distribution for modeling Bivariate count data. Its basic assumptions and marginal equi-dispersion, however, may prove limiting in some contexts. To allow for data dispersion, we develop here a Bivariate Conway-Maxwell-Poisson (COM-Poisson) distribution that includes the Bivariate Poisson, Bivariate Bernoulli, and Bivariate geometric distributions all as special cases. As a result, the Bivariate COM-Poisson distribution serves as a flexible alternative and unifying framework for modeling Bivariate count data, especially in the presence of data dispersion.

  • on the use of Bivariate mellin transform in Bivariate random scaling and some applications
    Methodology and Computing in Applied Probability, 2014
    Co-Authors: N Balakrishnan, A Stepanov
    Abstract:

    We discuss here the problem of Bivariate random scaling. Both direct and inverse problems of Bivariate random scaling are solved by two methods. While the first method is a distributional one, the second method is an indirect one associated with Bivariate Mellin transform. Finally, we use Bivariate random scaling for some statistical and simulational applications.

  • continuous Bivariate distributions
    2009
    Co-Authors: N Balakrishnan, C D Lai
    Abstract:

    Univariate distributions. - Bivariate copulas. - Distributions expressed as copulas. - Concepts of stochastic dependence. - Measures of dependence. - Constructions of Bivariate distributions.- Bivariate distributions constructed by conditional approach. - Variables in common method. - Bivariate gamma and related distributions. - Simple forms of the Bivariate density function. - Bivariate exponentional and related distributions. - Bivariate normal distribution. - Bivariate extreme value distributions. - Elliptically symmetric Bivariate distributions and other symmetric distributions. - Simulation of Bivariate observations.

  • property of Bivariate poisson distribution and its application to stochastic processes
    Statistics, 2004
    Co-Authors: B Chandrasekar, N Balakrishnan
    Abstract:

    Assuming that the random vectors X 1 and X 2 have independent Bivariate Poisson distributions, the conditional distribution of X 1 given X 1 + X 2 = n is obtained. The conditional distribution turns out to be a finite mixture of distributions involving univariate binomial distributions and the mixing proportions are based on a Bivariate Poisson (BVP) distribution. The result is used to establish two properties of a Bivariate Poisson stochastic process which are the Bivariate extensions of the properties for a Poisson process given by Karlin, S. and Taylor, H. M. (1975). A First Course in Stochastic Processes, Academic Press, New York.

Felix Famoye - One of the best experts on this subject based on the ideXlab platform.

  • on the Bivariate negative binomial regression model
    Journal of Applied Statistics, 2010
    Co-Authors: Felix Famoye
    Abstract:

    In this paper, a new Bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the Bivariate model are functions of the explanatory variables. The parameters of the Bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical data sets are used to illustrate the techniques. The BNBR model tends to perform better than the Bivariate Poisson regression model, but compares well with the Bivariate Poisson log-normal regression model.

  • a new Bivariate generalized poisson distribution
    Statistica Neerlandica, 2010
    Co-Authors: Felix Famoye
    Abstract:

    In this paper, a new Bivariate generalized Poisson distribution (GPD) that allows any type of correlation is defined and studied. The marginal distributions of the Bivariate model are the univariate GPDs. The parameters of the Bivariate distribution are estimated by using the moment and maximum likelihood methods. Some test statistics are discussed and one numerical data set is used to illustrate the applications of the Bivariate model.

Ioannis Ntzoufras - One of the best experts on this subject based on the ideXlab platform.

  • Bivariate poisson and diagonal inflated Bivariate poisson regression models in r
    Journal of Statistical Software, 2005
    Co-Authors: Dimitris Karlis, Ioannis Ntzoufras
    Abstract:

    In this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of Bivariate and diagonal inflated Bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance and implementation on simulated and real data sets using bivpois package is provided.

Setiawan, Dewi Indra - One of the best experts on this subject based on the ideXlab platform.

  • PENAKSIRAN PARAMETER DAN PENGUJIAN HIPOTESIS PADA GEOGRAPHICALLY WEIGHTED Bivariate GENERALIZED POISSON REGRESSION (Studi Kasus: Jumlah Kematian Bayi dan Jumlah Kematian Ibu di Jawa Timur tahun 2013)
    2017
    Co-Authors: Setiawan, Dewi Indra
    Abstract:

    Regresi poisson merupakan salah satu analisis regresi non linier yang variabel responnya mengikuti distribusi poisson. Pemodelan regresi poisson diperuntukkan hanya pada satu variabel respon disebut regresi univariat poisson, sedangkan pemodelan regresi poisson yang diperuntukkan pada dua variabel respon disebut regresi bivariat poisson. Model regresi poisson, baik regresi univariat poisson dan regresi bivariat poisson, memiliki asumsi spesifik, yaitu kesamaan antara rata-rata dan varians atau dikenal dengan istilah ekuidispersi. Apabila asumsi ini tidak terpenuhi akan menghasilkan kesimpulan yang tidak valid. Pelanggaran asumsi terjadi jika nilai rata-rata lebih besar daripada nilai varians (overdispersi). Regresi generalized poisson merupakan salah satu alternatif untuk mengatasi kasus overdispersi pada regresi Poisson. Bivariate Generalized Poisson Regression adalah pengembangan regresi bivariat poisson pada data yang mengalami kasus overdispersi. Pemodelan ini menghasilkan taksiran parameter yang bersifat global untuk seluruh lokasi (daerah). Adanya pengaruh lokasi yang merupakan faktor penting terhadap pemodelan apabila dilakukan di setiap daerah yang berbeda-beda. Geographically Weighted Bivariat Generalized Poisson (GWBGPR) adalah regresi bivariat generalized poisson yang mempertimbangkan efek spasial dimana data tersebut diambil. Kematian bayi dan kematian ibu merupakan dua hal yang saling terkait erat karena selama dalam kandungan ibu, janin sangat tergantung pada gizi yang dikonsumsi oleh ibunya. Analisis yang digunakan untuk memodelkan jumlah kematian bayi dan jumlah kematian ibu serta faktor-faktor yang mempengaruhinya ditiap kab/kota di Jawa Timur adalah GWBGPR. Penaksiran parameter model GWBGPR menggunakan MLE dengan metode iterasi Newton Raphson dan pengujian hipotesis mengunakan MLRT. Metode GWBGPR menghasilkan parameter yang berbeda-beda pada setiap lokasi. Variabel prediktor yang berpengaruh signifikan terhadap jumlah kematian bayi dan jumlah kematian ibu adalah presentase persalinan oleh tenaga kesehatan, presentase ibu hamil mendapatkan tablet Fe3 dan presentase wanita kawin dengan tingkat pendidikan SD kebawah. ====================================================================================================================== Poisson Regression is one of the non-linear regression models in response variables follow the Poisson distribution. Poisson regression model that are appropriate for modeling one response called univariate poisson regression and poisson regression model that are appropriate for modeling paired count data exhibiting correlation called Bivariate poisson regression model. Poisson regression model have a specific assumption, called equidispersion (equality of mean and variance), in practical applications and in “real” situations, this assumption is questionable since the variance can either be larger or smaller than the mean. If the variance is not equal to the mean, the estimation of poisson regression model are still consistent but inefficient, which leads to the invalidation of inference based on the estimated standard errors. Generalized poisson regression (GPR) has been found useful in fitting under-or overdispersed count data. Bivariate generalized poisson regression is a correlated Bivariate version of the univariate generalized poisson regression. Parameter estimation of BGPR model produces a global model for each observation location. Interpretation of this global model assumes that each location has the same characteristics but in some cases each location has different characteristics. The characteristics of each region is very likely affect the number of events in the region as well as the incidence of the Poisson distribution. Bivariate Generalized Poisson Regression model that notice the presence of spatial effects in the data called Geographically Weighted Bivariate Generalized Poisson Regression (GWBGPR). Infant mortality and maternal mortality are correlated at each other because during pregnancy, the fetus depends on the nutrient that is consumed by the mother. GWBGPR method will be applied for modelling maternal mortality and infant mortality in east java at 2013. Parameter estimation of GWBGPR model were done by using Maximum Likelihood Estimation (MLE) [4]. The parameter estimation of GWBGPR model using MLE method are not closed form so that the estimation process will be continued using newton raphson iteration. GWBGPR method produce local models to each observation location. Predictor that affected significantly to all groups for infant mortality and maternal mortality are percentage of deliveries by skilled health personnel, the percentage of pregnant women receiving tablets Fe3 and the percentage of married women with elementary educatio