On a multivariate gamma

Mathai, A. M.; Moschopoulos, P. G.

doi:10.1016/0047-259x(91)90010-y

Cited by 82 publications

(41 citation statements)

References 9 publications

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“…Thus, as suggested by Mathai and Moschopoulos (1991), the multivariate gamma distribution can be applied to check the impact that rain has on two uncorrelated streams. Considering the case in which these two uncorrelated streams pass through a town, rainfall may increase the chance of ‡ooding.…”

Section: Resultsmentioning

confidence: 99%

“…If information on the idiosyncratic gamma distributed term is available,   for  = 1      ¡ 1, the method of moments can applied. Otherwise, if only information on   is available, for  = 1      ¡ 1, one can apply the methodology suggested by Mathai and Moschopoulos (1991) for instance.…”

Section: Estimation Of Parametersmentioning

confidence: 99%

“…Here we follow the Mathai and Moschopoulos (1991) approach, which amongst other features, guarantees gamma distributed marginal densities.…”

Section: The Multivariate Gamma Distributionmentioning

confidence: 99%

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The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

Vitiello

Rebelo

2011

SSRN Journal

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In this paper we establish a Risk Neutral Valuation Relationship and develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy using a multivariate gamma distribution. In our framework, risk neutrality is obtained by using market equilibrium conditions, leading to preference-free contingent claim pricing equations. Multivariate contingent claim pricing models are of particular interest when payo¤s depend on two or more stochastic variables, such as options to exchange one asset for another, options on mutual funds, and options with a stochastic strike price in general. In our model each underlying stochastic variable depends on a systematic gamma distributed term and on an idiosyncratic one, where the former has a direct impact on the correlation structure of the underlying variables. To illustrate the applicability of our framework, we present multivariate gamma distributed versions of well-known multivariate normally/lognormally distributed contingent claim pricing formulae. The gamma distribution is particularly suitable to price stochastic variables that present implied volatilities that are an increasing function of the strike price.

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Section: Resultsmentioning

confidence: 99%

Section: Estimation Of Parametersmentioning

confidence: 99%

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The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

Vitiello

Rebelo

2011

SSRN Journal

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“…This distribution has the property that summation of two independent gamma-distributed random variables with the same scale still follows a gamma distribution, and the scale of a gamma distribution can be adjusted to any value with simple constant multiplication of the original random variable. Therefore, a bivariate gamma distribution whose components are positively correlated can be developed from linear combinations of independent gamma variables (Mathai and Moschopoulos, 1991). In addition, to serve the purpose of random effect in the survival model, the marginal means of both α 1 and α 2 need to be constrained at one.…”

Section: Choice For G(α 1 α 2 ): Bivariate Gamma Distributionmentioning

confidence: 99%

Accelerated failure time model for multivariate two-stage current-status data with parallel and longitudinal correlated random effects

Hsieh

Wang

2013

Statistics and Its Interface

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We develop a parametric accelerated failure time (AFT) model with random effects for analyzing multivariate twostage current-status survival data. This model structure is motivated by a breeding success study of common ravens in Rostock Germany around the year 1996. Association between land use and the stages of the two breeding eventshatching and fledgling-is of main research interest. Correlation among eggs within the same nest is modeled by a shared bivariate random-effect term, and the correlation of this bivariate random-effect term is designed to account for the dependency between the timing of two breeding events for the same egg. Analytically we construct the likelihood function and derive the maximum likelihood estimate with its asymptotic variance. In regression parameter estimation, the EM algorithm and a Monte Carlo version of the NewtonRaphson maximizer are adapted. A numerical study is also conducted to validate the likelihood based statistical inferences. In the real data analysis, no significant effect for land use was found for either stage. But low nest security in farmland might play some role in the fledgling stage, while food abundance in farmland is typically related positively to the breeding process.

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“…Several particular cases of these multivariate gamma densities including the bivariate cases have gained prominence over the years. Some examples include bivariate gamma distributions due to Cheriyan [3], Mathai and Moschopoulos [10], McKay [11], Kibble [8], Royen [14], Jensen [6], Sarmanov ([16], [17]). For an elaborate discussion of these distributions along with their applications, generalizations, method of construction and inter-relationships, one may refer to Balakrishnan and Lai [1], Samuel Kotz et al [15] and Yue et al [18] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Multivariate Gamma Distribution

Vaidyanathan

Lakshmi

2015

Stat., optim. inf. comput.

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Multivariate gamma distribution finds abundant applications in stochastic modelling, hydrology and reliability. Parameter estimation in this distribution is a challenging one as it involves many parameters to be estimated simultaneously. In this paper, the form of multivariate gamma distribution proposed by Mathai and Moschopoulos [9] is considered. This form has nice properties in terms of marginal and conditional densities. A new method of estimation based on optimal search is proposed for estimating the parameters using the marginal distributions and the concepts of maximum likelihood, spacings and least squares. The proposed methodology is easy to implement and is free from calculus. It optimizes the objective function by searching over a wide range of values and determines the estimate of the parameters. The consistency of the estimates is demonstrated in terms of mean, standard deviation and mean square error through simulation studies for different choices of parameters.

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On a multivariate gamma

Cited by 82 publications

References 9 publications

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

Accelerated failure time model for multivariate two-stage current-status data with parallel and longitudinal correlated random effects

Parameter Estimation in Multivariate Gamma Distribution

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