Pelican, Elena; Vernic, Raluca Maximum-likelihood estimation for the multivariate Sarmanov distribution: simulation study. (English) Zbl 1291.62080 Int. J. Comput. Math. 90, No. 9, 1958-1970 (2013). Summary: Used to model dependency in a multivariate setting with given marginals, Sarmanov’s family of distributions creates difficulties when it comes to statistical inference. In this paper, we study maximum-likelihood procedures for estimating Sarmanov’s distribution parameters for two different models: Under model I, we make use of a random data sample of volume \(m\) observed from an \(n\)-dimensional random vector, while model II consists of the first \(n\) dependent univariate random variables from a discrete-time stochastic process to which we try to fit Sarmanov’s distribution starting from the corresponding \(n\)-tuple of observed values. To estimate some specific parameters, the use of the method of moments based on the covariance/correlation coefficient is also suggested. We illustrate these methods on simulated data and discuss the results. Cited in 6 Documents MSC: 62G05 Nonparametric estimation 62H12 Estimation in multivariate analysis 65C10 Random number generation in numerical analysis Keywords:Sarmanov distribution; parameters estimation; maximum-likelihood method; method of moments; data simulation PDFBibTeX XMLCite \textit{E. Pelican} and \textit{R. Vernic}, Int. J. Comput. Math. 90, No. 9, 1958--1970 (2013; Zbl 1291.62080) Full Text: DOI References: [1] DOI: 10.1016/j.insmatheco.2009.08.002 · Zbl 1231.91141 [2] DOI: 10.1073/pnas.17.12.656 · Zbl 0003.25602 [3] DOI: 10.1063/1.526462 · Zbl 0566.60013 [4] DOI: 10.1287/mksc.1090.0491 [5] DOI: 10.1016/j.insmatheco.2009.07.002 · Zbl 1231.91198 [6] Isaacson E., Analysis of Numerical Methods (1966) · Zbl 0168.13101 [7] DOI: 10.1002/0471722065 [8] DOI: 10.1080/03610929608831759 · Zbl 0875.62205 [9] Nelsen R., An Introduction to Copulas (2006) · Zbl 1152.62030 [10] Sarmanov, O. V. 1966.Generalized normal correlation and two-dimensional Frechet classes, Vol. 168, 596–599. Doclady: Soviet Mathematics. [11] DOI: 10.1287/mksc.1070.0328 [12] DOI: 10.1081/STA-120029824 · Zbl 1114.62334 [13] Tang, Q., Vernic, R. and Yuan, Z. 2010.The finite-time ruin probability in the presence of heavy-tailed claims and dependent return rates on risky investment3–6. 6th Conference in Actuarial Science & Finance on Samos, June [14] Vernic, R. 2008.On Sarmanov’s distribution and the asymptotic ultimate ruin probability273–281. Constanta Proceedings of the 7th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, October 22–25 [15] DOI: 10.1017/CBO9780511755392 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.