A new asymmetric class of bivariate copulas for modeling dependence

In this paper, we propose an asymmetric class of bivariate copulas. This class is obtained through limiting properties of the extended copula introduced by Bekrizadeh, et al. (2015 Bekrizadeh, H., Parham, G. A., Zadkarami, M. R. (2015). Extending some classes of copulas; Applications. Ph.D. Thesis, University of Shahid Chamran, Ahvaz. [Google Scholar]), and includes some of known copulas. Some general formulas for well-known association measures and concepts of dependence of the proposed model are obtained. This paper highlights the usefulness of this new bivariate copula for modeling the interested variables whose marginal distribution effect on joint distribution isn't identical. We apply some subfamilies of this new class to model a dataset of medical science to show the superiority of presented model in comparison with the known copulas. These results will be investigated using simulation.     

Aging and ordering properties of multivariate lifetimes with Archimedean dependence structures

This paper further studies monotone aging properties of the multivariate random lifetime. We revise the sufficient condition for the negative monotone aging property in terms of the multivariate usual stochastic order in Theorem 3.3 of Rezapour et al. (2013) Rezapour, M., Alamatsaz, M.H., Pellerey, F. (2013). Multivariate aging with Archimedean dependence structures in high dimensions. Commun. Stat. - Theory Methods 42:2056–2070.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] and derive the condition sufficient to the multivariate monotone aging properties in terms of the upper orthant order. Also we study the upper orthant order of multivariate residual lifetimes and inactivity times from populations sharing a common Archimedean survival copula and Archimedean survival copula, respectively. Two simple applications in multivariate stress-strength and frailty models are presented as well.     

Multivariate Aging with Archimedean Dependence Structures in High Dimensions

Bivariate aging notions for a vector X of lifetimes based on stochastic comparisons between X and X _t, where X _t is the multivariate residual lifetime after time t > 0, have been studied in Pellerey (2008 Pellerey , F. ( 2008 ). On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas . Kybernetika 44 : 795 – 806 .[Web of Science ®] , [Google Scholar]) under the assumption that the dependence structure in X is described by an Archimedean survival copula. Similar stochastic comparisons between X _t and X _t+s, for all t; s > 0, were considered in Mulero and Pellerey (2010 Mulero , J. , Pellerey , F. ( 2010 ). Bivariate aging properties under Archimedean dependence structures . Commun. Statist. Theor. Meth. 39 : 3108 – 3121 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In this article, these results are generalized and extended to the multivariate case. Two illustrative examples are also provided.     

A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries

In Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]), the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developed in Bielecki et al. (2014b Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014b ). A bottom-up dynamic model of portfolio credit risk - Part I: Markov copula perspective . In: Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574) . [Google Scholar],c) where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic default intensities and random recoveries in the bottom-up modeling framework of Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]) while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives (Assefa et al., 2011 Assefa , S. , Bielecki , T. R. , Crépey , S. , Jeanblanc , M. ( 2011 ). CVA computation for counterparty risk assessment in credit portfolios . In: Bielecki , T.R. , Brigo , D. , Patras , F. , Eds., Credit Risk Frontiers . Hoboken : Wiley/Bloomberg-Press . [Google Scholar]; Bielecki et al., 2012 Bielecki , T. R. , Crépey , S. , Jeanblanc , M. , Zargari , B. ( 2012 ). Valuation and Hedging of CDS counterparty exposure in a markov copula model . Int. J. Theoret. Appl. Fin. 15 ( 1 ): 1250004 .[Crossref] , [Google Scholar]), as CVA is sensitive to the stochastic nature of credit spreads and random recoveries allow to achieve satisfactory calibration even for “badly behaved” data sets. This article is thus a complement to Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]), Bielecki et al. (2014b Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014b ). A bottom-up dynamic model of portfolio credit risk - Part I: Markov copula perspective . In: Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574) . [Google Scholar]) and Bielecki et al. (2014c Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014c ). A bottom-up dynamic model of portfolio credit risk - Part II: Common-shock interpretation, calibration and hedging issues . Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.2245130) . [Google Scholar]).     

Tail Behavior and Extremes of Short-Tailed Symmetric Distribution

Tiku and Vaughan (1999 Tiku , M. L. , Vaughan , D. C. ( 1999 ). A Family of Short-tailed Symmetric Distributions. Technical Report, McMaster University, Canada . [Google Scholar]) introduced a short-tailed symmetric family recently. In the article, the tail properties of the short-tailed symmetric distribution are studied and the asymptotic distribution of the maximum of i.i.d. random variables obeying the short-tailed distribution is gained.     

Further Results for a General Family of Bivariate Copulas

A bivariate family of copulas has been initiated by Cuadras-Augé (1981 Cuadras, C.M., Augé, J. (1981). A continuous general multivariate distribution and its properties. Commun. Statist. (A) Theor. Meth. 10:339–353.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Marshall (1996 Marshall, A.W. (1996). Copulas, marginals, and joint distributions. In: Distributions with fixed marginals and related topics. IMS Lecture Notes Monogr. Ser. 28:213–222.[Crossref] , [Google Scholar]). Recently, Durante (2007 Durante, F. (2007). A new family of symmetric bivariate copulas. C. R. Math. Acad. Sci. Paris 344:195–198.[Crossref], [Web of Science ®] , [Google Scholar]) considered this family as a general family of symmetric bivariate copulas indexed by a generator function and studied some of its dependence properties. In this article, we obtain and describe further aspects of dependence for this family. For example, we have proved that the family has positive likelihood ratio dependence structure if and only if the family reduces to some well-known copulas. We also derive several proper forms for the generator function of this family. Considering a multivariate extension of the bivariate family of copulas provided by Durante et al. (2007 Durante, F., Quesada-Molina, J.J., Flores, M. (2007). On a family of multivariate copulas for aggregation processes. Inform. Sci. 177(24):5715–5724.[Crossref], [Web of Science ®] , [Google Scholar]), some dependence properties are studied. Finally, some positive dependence stochastic orderings for two random vectors having a copula from the proposed families, are discussed.     

Bayesian bivariate survival analysis using the power variance function copula

Copula models have become increasingly popular for modelling the dependence structure in multivariate survival data. The two-parameter Archimedean family of Power Variance Function (PVF) copulas includes the Clayton, Positive Stable (Gumbel) and Inverse Gaussian copulas as special or limiting cases, thus offers a unified approach to fitting these important copulas. Two-stage frequentist procedures for estimating the marginal distributions and the PVF copula have been suggested by Andersen (Lifetime Data Anal 11:333–350, 2005), Massonnet et al. (J Stat Plann Inference 139(11):3865–3877, 2009) and Prenen et al. (J R Stat Soc Ser B 79(2):483–505, 2017) which first estimate the marginal distributions and conditional on these in a second step to estimate the PVF copula parameters. Here we explore an one-stage Bayesian approach that simultaneously estimates the marginal and the PVF copula parameters. For the marginal distributions, we consider both parametric as well as semiparametric models. We propose a new method to simulate uniform pairs with PVF dependence structure based on conditional sampling for copulas and on numerical approximation to solve a target equation. In a simulation study, small sample properties of the Bayesian estimators are explored. We illustrate the usefulness of the methodology using data on times to appendectomy for adult twins in the Australian NH&MRC Twin registry. Parameters of the marginal distributions and the PVF copula are simultaneously estimated in a parametric as well as a semiparametric approach where the marginal distributions are modelled using Weibull and piecewise exponential distributions, respectively.     

On an Extended Version of Skew Generalized Normal Distribution and Some of its Properties

Abstract

A generalization of Chauvenet's test (see Bol'shev, L. N. 1969 Bol'shev, L. N. 1969. On tests for rejecting outlying observations. Trudy In-ta prikladnoi Mat. Tblissi Gosudart. univ., 2: 159–177. (In Russian) [Google Scholar]. On tests for rejecting outlying observations. Trudy In-ta prikladnoi Mat. Tblissi Gosudart. univ. 2:159–177. (In Russian); Voinov, V. G., Nikulin, M. N. 1996 Voinov, V. G. and Nikulin, M. N. 1996. Unbaised Estimators and Their Applications Vol. 2, Kluwer Academic Publishers.  [Google Scholar]. Unbaised Estimators and Their Applications. Vol. 2. Kluwer Academic Publishers.) suitable to applied the problem of detecting r outliers in an univariate data set is proposed. In the exponential case, the Chauvenet's test can be used. Various modifications of this test were considered by Bol'shev, Ibrakimov and Khalfina (Ibrakimov, I. A., Khalfina 1978 Ibrakimov, I. A. and Khalfina. 1978. Some asymptotic results concerning the Chauvenet test. Ter. Veroyatnost. i Primenen., 23(3): 593–597.  [Google Scholar]. Some asymptotic results concerning the Chauvenet test. Ter. Veroyatnost. i Primenen. 23(3):593–597.), Greenwood and Nikulin (Greenwood, Nikulin, P. E. 1996 Greenwood and Nikulin, P. E. 1996. A Guide to Chi-Squared Testing New York: John Wiley and Sons, Inc..  [Google Scholar]. A Guide to Chi-Squared Testing. New York: John Wiley and Sons, Inc.) depending on the choice of the estimation method used: MLE or MVUE. As procedures for testing one outlier in exponential model have been investigated by a number of authors including Chikkagoudar and Kunchur (Chikkagoudar, M. S., Kunchur, S. H. 1983 Chikkagoudar, M. S. and Kunchur, S. H. 1983. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth., 12: 2127–2142. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127–2142.), Lewis and Fieller (Lewis, T., Fiellerm N. R. J. 1979 Lewis, T. and Fiellerm, N. R. J. 1979. A recursive algorithm for null distribution for outliers: I. Gamma samples. Technometrics, 21: 371–376. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. A recursive algorithm for null distribution for outliers : I. Gamma samples. Technometrics 21:371–376.), Likes (Likes, J. 1966 Likes, J. 1966. Distribution of Dixon's statistics in the case of an exponential population. Metrika, 11: 46–54. (91, 96, 136, 198–200, 204, 209, 210)[Crossref] , [Google Scholar]. Distribution of Dixon's statistics in the case of an exponential population. Metrika 11:46–54. (91, 96, 136, 198–200, 204, 209, 210).) and Kabe (Kabe, D. G. 1970 Kabe, D. G. 1970. Testing outliers from an exponential population. Metrika, 15: 15–18. [Crossref], [Web of Science ®] , [Google Scholar]. Testing outliers from an exponential population. Metrika 15:15–18.); only two types of statistics for testing multiple outliers exist. First is Dixon's while the second is based on the ratio of the sum of the observations suspected to be outliers to the sum of all observations of the sample. In fact, most of these authors have considered a general case of gamma model and the results for exponential model are given a special case. The object of the present communication is to focus on alternative models, namely slippage alternatives (see Barnett, Vic., Toby Lewis 1978 Barnett, Vic. and Toby, Lewis. 1978. Outlier in Statistical Data New York: John Wiley and Sons, Inc..  [Google Scholar]. Outlier in Statistical Data. New York: John Wiley and Sons, Inc.) in exponential samples. We propose a statistic different from the well known Dixon's statistic D_r to test for multiple outliers. Distribution of the test based on this new statistic under slippage alternatives is obtained and hence the tables of critical values are given, for various n (size of the sample) and r (the number of outliers). The power of the new test is also calculated, it is compared to the power of the Dixon's statistic (Chikkagoudar, M. S., Kunchur, S. H. 1983 Chikkagoudar, M. S. and Kunchur, S. H. 1983. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth., 12: 2127–2142. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127–2142.). Notice that the new statistic based test power is greater the Dixon's statistic based test one.     

On dynamic weighted survival entropy of order α

Recently, Abbasnejad et al. (2010 Abbasnejad, M., Arghami, N.R., Morgenthaler, S., Mohtashami Borzadaran, G.R. (2010). On the dynamic survival entropy. Stat. Probab. Lett. 80:1962–1971.[Crossref], [Web of Science ®] , [Google Scholar]) proposed a measure of uncertainty based on survival function, called the survival entropy of order α. A dynamic form of the survival entropy of order α is also proposed by them. In this paper, we derive the weighted form of these measures. The properties of the new measures are also discussed.     

Methods for Bivariate Survival Data with Mismeasured Covariates Under an Accelerated Failure Time Model

Accelerated failure time models are useful in survival data analysis, but such models have received little attention in the context of measurement error. In this paper we discuss an accelerated failure time model for bivariate survival data with covariates subject to measurement error. In particular, methods based on the marginal and joint models are considered. Consistency and efficiency of the resultant estimators are investigated. Simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring the measurement error of covariates. As an illustration we apply the proposed methods to analyze a data set arising from the Busselton Health Study (Knuiman et al., 1994 Knuiman , M. W. , Cullent , K. J. , Bulsara , M. K. , Welborn , T. A. , Hobbs , M. S. T. ( 1994 ). Mortality trends, 1965 to 1989, in Busselton, the site of repeated health surveys and interventions . Austral. J. Public Health 18 : 129 – 135 . [CSA] [Crossref], [PubMed] , [Google Scholar]).     

New Approach of Directional Dependence in Exchange Markets Using Generalized FGM Copula Function

This article presents an application of copula methodology in exchange markets. In this article, we consider the concept of directional dependence given by Sungur (2005 Sungur , E. A. ( 2005 ). Some observations on copula regression functions . Communications in Statistics—Theory and Methods 34 : 1967 – 1978 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We also consider and study directional dependence for generalized Farlie–Gumbel–Morgenstern (FGM) distributions, which are a member of the Rodríguez-Lallena and Úbeda-Flores (2004 Rodríguez-Lallena , J. A. , Úbeda-Flores , M. ( 2004 ). A new class of bivariate copulas . Statistical Probability Letters 66 : 315 – 325 .[Crossref], [Web of Science ®] , [Google Scholar]) family, C(u, v) = uv + f(u)g(v). Examples of the generalized FGM distributions are provided with exchange market data of the Euro, Canadian dollar, Korean Won, Japanese Yen, and Hong Kong dollar against the U.S. dollar.     

Some Fundamental Properties of a Multivariate von Mises Distribution

In application areas like bioinformatics, multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modeling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2012 Mardia , K. V. , Kent , J. T. , Zhang , Z. , Taylor , C. , Hamelryck , T. ( 2012 ). Mixtures of concentrated multivariate sine distributions with applications to bioinformatics . J. Appl. Stat. 39 : 2475 – 2492 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.     

The Finite Time Ruin Probability of a New Risk Model Based on Entrance Process

In this article, we consider a new insurance risk model based on the entrance process proposed in Li et al. (2005 Li , Z. , Zhu , J. , Chen , F. ( 2005 ). Study of a risk model based on the entrance process . Statist. Probab. Lett. 72 : 1 – 10 .[Crossref], [Web of Science ®] , [Google Scholar]), and investigate the finite time ruin probabilities of this model. It is showed that an exponential upper bound for the finite time ruin probability exists, when the distributions of the claim size are light tailed. Furthermore, when the distributions of the claim size are heavy tailed, an asymptotic formula for the finite time ruin probability is obtained.     

An approximation to the convolution of gamma distributions

In general, the exact distribution of a convolution of independent gamma random variables is quite complicated and does not admit a closed form. Of all the distributions proposed, the gamma-series representation of Moschopoulos (1985 Moschopoulos, P. G. (1985). The distribution of the sum of independent gamma random variables. Annals of the Institute of Statistical Mathematics 37Part A:541–544. [Google Scholar]) is relatively simple to implement but for particular combinations of scale and/or shape parameters the computation of the weights of the series can result in complications with too much time consuming to allow a large-scale application. Recently, a compact random parameter representation of the convolution has been proposed by Vellaisamy and Upadhye (2009 Vellaisamy, P., Upadhye, N. S. (2009). On the sums of compound negative binomial and gamma random variables. Journal of Applied Probability 46:272–283.[Crossref], [Web of Science ®] , [Google Scholar]) and it allows to give an exact interpretation to the weights of the series. They describe an infinite discrete probability distribution. This result suggested to approximate Moschopoulos’s expression looking for an approximating theoretical discrete distribution for the weights of the series. More precisely, we propose a general negative binomial distribution. The result is an “excellent” approximation, fast and simple to implement for any parameter combination.     

Characterizations of the General Multivariate Weibull Distributions

For studying and modeling the time to failure of a system or component, many reliability practitioners used the hazard rate and its monotone behaviors. However, nowadays, there are two problems. First, the modern components have high reliability and, second, their distributions are usually have non monotone hazard rate, such as, the truncated normal, Burr XII, and inverse Gaussian distributions. So, modeling these data based on the hazard rate models seems to be too stringent. Zimmer et al. (1998 Zimmer , W. J. , Wang , Y. , Pathak , P. K. ( 1998 ). Log-odds rate and monotone log-odds rate distributions . J. Qual. Technol. 30 ( 4 ): 376 – 385 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Wang et al. (2003 Wang , Y. , Hossain , A. M. , Zimmer , W. J. ( 2003 ). Monotone log-odds rate distributions in reliability analysis . Commun. Statist. Theor. Meth. 32 ( 11 ): 2227 – 2244 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 2008 Wang , Y. , Hossain , A. M. , Zimmer , W. J. ( 2008 ). Useful properties of the three-parameter Burr XII distribution. In: Ahsanullah M., Applied Statistics Research Progress. pp. 11–20 . [Google Scholar]) introduced and studied a new time to failure model in continuous distributions based on log-odds rate (LOR) which is comparable to the model based on the hazard rate.

There are many components and devices in industry, that have discrete distributions with non monotone hazard rate, so, in this article, we introduce the discrete log-odds rate which is different from its analog in continuous case. Also, an alternative discrete reversed hazard rate which we called it the second reversed rate of failure in discrete times is also defined here. It is shown that the failure time distributions can be characterized by the discrete LOR. Moreover, we show that the discrete logistic and log logistics distributions have property of a constant discrete LOR with respect to t and ln t, respectively. Furthermore, properties of some distributions with monotone discrete LOR, such as the discrete Burr XII, discrete Weibull, and discrete truncated normal are obtained.     

Comparison of Frailty Models for Acute Leukemia Data under Gompertz Baseline Distribution

In this article, we consider two different shared frailty regression models under the assumption of Gompertz as baseline distribution. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we consider the inverse Gaussian shared frailty model also. We compare these two models to a real life bivariate survival data set of acute leukemia remission times (Freireich et al., 1963 Freireich, E.J., Gehan, E., Frei, E., Schroeder, L.R., Wolman, I.J., Anbari, R., Burgert, E.O., Mills, S.D., Pinkel, D., Selawry, O.S., Moon, J.H., Gendel, B.R., Spurr, C.L., Storrs, R., Haurani, F., Hoogstraten, B., Lee, S. (1963). The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: a model for evaluation of other potentially useful therapy. Blood 21:699–716.[Web of Science ®] , [Google Scholar]). Analysis is performed using Markov Chain Monte Carlo methods. Model comparison is made using Bayesian model selection criterion and a well-fitted model is suggested for the acute leukemia data.     

Fiducial distribution in a power series family

Abstract

In this article the interest is on finding the fiducial distribution of the parameter, when the probability distribution belongs to the power series family, as in Johnson et al. (1992 Johnson, N. L., S. Kotz, and A. W. Kemp. 1992. Univariate discrete distributions. New York, NY: John Wiley and Sons. [Google Scholar]). Recently in Nájera and O’Reilly (2017 Nájera, E., and F. O’Reilly. 2017. On fiducial generators. Communications Statistics - Theory Methods 46 (5):2232–2248. doi:10.1080/03610926.2015.1040505.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) an argument is given to obtain a unique fiducial in the Bernoulli case. An attempt is made here to define some sort of invariance in a power series distribution so that, as was done in the Bernoulli case, one may find a unique invariant fiducial for the parameter. The Bernoulli case is reviewed in detail and the Poisson and negative binomial cases are addressed.     

Baker- Lin-Huang Type Bivariate Distributions Based on Order Statistics

Baker (2008 Baker, R. (2008). An order-statistics-based method for constructing multivariate distributions with fixed marginals. J. Multivariate Anal. 99: 23122327.[Crossref], [Web of Science ®] , [Google Scholar]) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin and Huang (2010 Lin, G.D., Huang, J.S. (2010). A note on the maximum correlation for Baker’s bivariate distributions with fixed marginals. J. Multivariate Anal. 101: 22272233.[Crossref], [Web of Science ®] , [Google Scholar]) discovered an important property of Baker’s distribution and showed that the Pearson’s correlation coefficient for this distribution converges to maximum attainable value, i.e., the correlation coefficient of the Fréchet upper bound, as n increases to infinity. Bairamov and Bayramoglu (2013 Bairamov, I., Bayramoglu, K. (2013). From Huang-Kotz distribution to Baker’s distribution. J. Multivariate Anal. 113: 106115.[Crossref], [Web of Science ®] , [Google Scholar]) investigated a new class of bivariate distributions constructed by using Baker’s model and distributions of order statistics from dependent random variables, allowing higher correlation than that of Baker’s distribution. In this article, a new class of Baker’s type bivariate distributions with high correlation are constructed based on distributions of order statistics by using an arbitrary continuous copula instead of the product copula.