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Journal articles on the topic 'Farlie-Gumbel-Morgenstern family of bivariate distributions'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

El-Morshedy, M., Fahad Sameer Alshammari, Yasser S. Hamed, Mohammed S. Eliwa, and Haitham M. Yousof. "A New Family of Continuous Probability Distributions." Entropy 23, no. 2 (2021): 194. http://dx.doi.org/10.3390/e23020194.

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In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to e

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Refaie, Mohamed. "A New Family of Continuous Distributions: Properties, Copulas and Real Life Data Modeling." Statistics, Optimization & Information Computing 9, no. 3 (2021): 748–68. http://dx.doi.org/10.19139/soic-2310-5070-1130.

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A new family of distributions called the Kumaraswamy Rayleigh family is defied and studied. Some of its relevant statistical properties are derived. Many new bivariate type G families using the of Farlie-Gumbel-Morgenstern, modified Farlie-Gumbel-Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. The method of the maximum likelihood estimation is used. Some special models based on log-logistic, exponential, Weibull, Rayleigh, Pareto type II and Burr type X, Lindley distributions are presented and studied. Three dimensional skewness and kurtosis plots are presented. A gr

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3

Gupta, Ramesh C. "Reliability characteristics of Farlie–Gumbel–Morgenstern family of bivariate distributions." Communications in Statistics - Theory and Methods 45, no. 8 (2015): 2342–53. http://dx.doi.org/10.1080/03610926.2013.828075.

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Attwa, Rasha Abd-Elwahaab, Taha Radwan, and Esraa Osama Abo Zaid. "Bivariate q-extended Weibull morgenstern family and correlation coefficient formulas for some of its sub-models." AIMS Mathematics 8, no. 11 (2023): 25325–42. http://dx.doi.org/10.3934/math.20231292.

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<abstract><p>A bivariate extension of a flexible univariate family is proposed. The new family is called bivariate q-extended Weibull Morgenstern family of distributions which can be constructed based on the Farlie-Gumbel-Morgenstern (FGM) copula technique. After introducing the new family, four sub-models are discussed in detail from the theoretical and numerical coefficient of correlation point of view with pointing to the effect of the $ q $ parameter.</p></abstract>

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Shrahili, Mansour, and Naif Alotaibi. "A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times." Symmetry 12, no. 9 (2020): 1462. http://dx.doi.org/10.3390/sym12091462.

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A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model pa

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Cuadras, Carles M., and Walter Díaz. "Another generalization of the bivariate FGM distribution with two-dimensional extensions." Acta et Commentationes Universitatis Tartuensis de Mathematica 16, no. 1 (2012): 3–12. http://dx.doi.org/10.12697/acutm.2012.16.01.

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The Farlie–Gumbel–Morgenstern family of bivariate distributions with given marginals is frequently used in theory and applications and has been generalized in many ways. With the help of two auxiliary distributions, we propose another generalization and study its properties. After defining the dimension of a distribution as the cardinal of the set of canonical correlations, we prove that some well-known distributions are practically two-dimensional. Then we introduce an extended FGM family in two dimensions and study how to approximate any distribution to this family.

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Ahmadi, Jafar, and M. Fashandi. "Characterization of symmetric distributions based on concomitants of ordered variables from FGMs family of bivariate distributions." Filomat 33, no. 13 (2019): 4239–50. http://dx.doi.org/10.2298/fil1913239a.

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Several characterization results of a symmetric distribution based on concomitants of order statistics as well as k-records from Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions are established. These include characterizations of a symmetric distribution on the basis of equality in distribution, moments, R?nyi and Tsallis entropies of concomitants of upper and lower order statistics, also in terms of the same properties of concomitants of upper and lower k-records.

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Cuadras, Carles M. "On Bivariate Distributions with Singular Part." Axioms 13, no. 7 (2024): 433. http://dx.doi.org/10.3390/axioms13070433.

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There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass on a curve. We define a general condition useful to detect the singular part of a distribution. By continuous extension of the bivariate diagonal expansion, we define and study a wide family containing these singular distributions, obtain the probability density, and find the canonical correlati

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Alawady, M. A., H. M. Barakat, Shengwu Xiong, and M. A. Abd Elgawad. "On concomitants of dual generalized order statistics from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions." Asian-European Journal of Mathematics 14, no. 10 (2021): 2150185. http://dx.doi.org/10.1142/s1793557121501850.

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In this paper, we study the concomitants of [Formula: see text]-dual generalized order statistics ([Formula: see text]-DGOS) from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions as an extension of several recent papers. This study can also be applied to the model of [Formula: see text]-generalized order statistics ([Formula: see text]-GOS) as a parallel model of [Formula: see text]-DGOS. Furthermore, the joint distribution of [Formula: see text]-DGOS of concomitants for this family is studied. Some useful recurrence relations between single and product moments of concomit

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Husseiny, Islam A., Metwally A. Alawady, Salem A. Alyami, and Mohamed A. Abd Elgawad. "Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family." Mathematics 11, no. 6 (2023): 1377. http://dx.doi.org/10.3390/math11061377.

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In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressi

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Nagy, M., and Yusra A. Tashkandy. "Weighted Extropy for Concomitants of Upper k-Record Values Based on Huang–Kotz Morgenstern of Bivariate Distribution." Journal of Mathematics 2023 (September 4, 2023): 1–15. http://dx.doi.org/10.1155/2023/3423690.

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In this paper, the marginal distribution of concomitants of k − record values (CKR) based on the Huang–Kotz Farlie–Gumbel–Morgenstern (HK-FGM) family of bivariate distributions is derived. In addition, we obtained the joint distribution of CKR for this family. Also, we obtained the hazard rate, reversed hazard rate, and residual life functions of CKR using the HK-FGM family. The weighted extropy and the weighted cumulative past extropy (WCPJ) are acquired for CKR under the HK-FGM family. In addition, we look into the issue of estimating the WCPJ by combining the empirical method with the concu

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Fayomi, Aisha, Ehab M. Almetwally, and Maha E. Qura. "A novel bivariate Lomax-G family of distributions: Properties, inference, and applications to environmental, medical, and computer science data." AIMS Mathematics 8, no. 8 (2023): 17539–84. http://dx.doi.org/10.3934/math.2023896.

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<abstract><p>This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull

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Abd Elgawad, Mohamed A., Haroon M. Barakat, Doaa A. Abd El-Rahman, and Salem A. Alyami. "Scrutiny of a More Flexible Counterpart of Huang–Kotz FGM’s Distributions in the Perspective of Some Information Measures." Symmetry 15, no. 6 (2023): 1257. http://dx.doi.org/10.3390/sym15061257.

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In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. Moreover, some useful recurrence relations between single and product moments of concomitants are obtained. In addition, the asymptotic behavior of the concomitant’s rank for order statistics (OSs) is studied. The information measures, differential entropy, Kullback–Leibler (KL) distance, Fish

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Barakat, H. M., E. M. Nigm, and A. H. Syam. "Concomitants of order statistics and record values from Bairamov-Kotz-Becki-FGM bivariate-generalized exponential distribution." Filomat 32, no. 9 (2018): 3313–24. http://dx.doi.org/10.2298/fil1809313b.

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We introduce the Bairamov-Kotz-Becki-Farlie-Gumble-Morgenstern (BKB-FGM) type bivariategeneralized exponential distribution. Some distributional properties of concomitants of order statistics as well as record values for this family are studied. Recurrence relations between the moments of concomitants are obtained, some of these recurrence relations were not publishes before for Morgenstern type bivariate distributions. Moreover, most of the paper results are extended to arbitrary distributions (see Remark 3.1).

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Husseiny, I. A., M. Nagy, A. H. Mansi, and M. A. Alawady. "Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution." AIMS Mathematics 9, no. 9 (2024): 23268–90. http://dx.doi.org/10.3934/math.20241131.

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<p>Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis e

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Fayomi, Aisha, Ehab M. Almetwally, and Maha E. Qura. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions." Mathematics 11, no. 13 (2023): 2986. http://dx.doi.org/10.3390/math11132986.

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In survival analyses, infections at the catheter insertion site among kidney patients using portable dialysis machines pose a significant concern. Understanding the bivariate infection recurrence process is crucial for healthcare professionals to make informed decisions regarding infection management protocols. This knowledge enables the optimization of treatment strategies, reduction in complications associated with infection recurrence and improvement of patient outcomes. By analyzing the bivariate infection recurrence process in kidney patients undergoing portable dialysis, it becomes possi

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Nagy, M., H. M. Barakat, M. A. Alawady, et al. "Inference and other aspects for $ q- $Weibull distribution via generalized order statistics with applications to medical datasets." AIMS Mathematics 9, no. 4 (2024): 8311–38. http://dx.doi.org/10.3934/math.2024404.

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<abstract><p>This work utilizes generalized order statistics (GOSs) to study the $ q $-Weibull distribution from several statistical perspectives. First, we explain how to obtain the maximum likelihood estimates (MLEs) and utilize Bayesian techniques to estimate the parameters of the model. The Fisher information matrix (FIM) required for asymptotic confidence intervals (CIs) is generated by obtaining explicit expressions. A Monte Carlo simulation study is conducted to compare the performances of these estimates based on type Ⅱ censored samples. Two well-established measures of inf

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ABD ELGAWAD, M. A., H. M. BARAKAT, M. M. ABDELWAHAB, M. A. ZAKY, and I. A. HUSSEINY. "Fisher Information and Shannon’s Entropy for Record Values and Their Concomitants under Iterated FGM Family." Romanian Journal of Physics 69, no. 1-2 (2024): 103. http://dx.doi.org/10.59277/romjphys.2024.69.103.

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Let {(Xi ,Yi), i ≥ 1} be independent and identically distributed random variables (RVs) from a continuous bivariate distribution. If {Rn,n ≥ 1} is the sequence of upper record values in the sequence {Xi}, then the RV Yi, which corresponds to Rn is called the concomitant of the nth record, denoted by R[n]. We study the Shannon entropy (SHANE) of R[n] and (Rn,R[n]) under iterated Farlie-Gumbel-Morgenstern (IFGM) family. In addition, we find the Kullback-Leibler distance (K-L) between R[n] and Rn. Moreover, we study the Fisher information matrix (FIM) for record values and their concomitants abou

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Arun, Sasikumar Padmini, Christophe Chesneau, Radhakumari Maya, and Muhammed Rasheed Irshad. "Farlie–Gumbel–Morgenstern Bivariate Moment Exponential Distribution and Its Inferences Based on Concomitants of Order Statistics." Stats 6, no. 1 (2023): 253–67. http://dx.doi.org/10.3390/stats6010015.

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In this research, we design the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, a bivariate analogue of the moment exponential distribution, using the Farlie–Gumbel–Morgenstern approach. With the analysis of real-life data, the competitiveness of the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution in comparison with the other Farlie–Gumbel–Morgenstern distributions is discussed. Based on the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, we develop the distribution theory of concomitants of order statistics and derive the best line

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Yan, Rongfang, Yinping You, and Xiaohu Li. "On bivariate ageing properties of exchangeable Farlie–Gumbel–Morgenstern distributions." Communications in Statistics - Theory and Methods 46, no. 23 (2017): 11843–53. http://dx.doi.org/10.1080/03610926.2017.1285927.

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Šeliga, Adam, Manuel Kauers, Susanne Saminger-Platz, Radko Mesiar, Anna Kolesárová, and Erich Peter Klement. "Polynomial bivariate copulas of degree five: characterization and some particular inequalities." Dependence Modeling 9, no. 1 (2021): 13–42. http://dx.doi.org/10.1515/demo-2021-0101.

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Abstract Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a, b, c), i.e., to some set of polynomials in two variables of degree 1: p(x, y) = ax + by + c. The set of the parameters yielding a copula is characterized and visualized in detail. Polynomial copulas of degree 5 satisfying particular (in)equalities (symmetry, Schur concavity, positive and negative quadrant dependence, ultramodularity) are discussed and characterized. Then it is shown that for polynomial co

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Asadi, Majid, Somayeh Ashrafi, Nader Ebrahimi, and Ehsan S. Soofi. "MODELS BASED ON PARTIAL INFORMATION ABOUT SURVIVAL AND HAZARD GRADIENT." Probability in the Engineering and Informational Sciences 24, no. 4 (2010): 561–84. http://dx.doi.org/10.1017/s0269964810000185.

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This article develops information optimal models for the joint distribution based on partial information about the survival function or hazard gradient in terms of inequalities. In the class of all distributions that satisfy the partial information, the optimal model is characterized by well-known information criteria. General results relate these information criteria with the upper orthant and the hazard gradient orderings. Applications include information characterizations of the bivariate Farlie–Gumbel–Morgenstern, bivariate Gumbel, and bivariate generalized Gumbel, for which no other infor

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George, Alphonsa, and Dais George. "DISCRETIZED POISSON-EXPONENTIATED WEIBULL DISTRIBUTION AND ITS APPLICATIONS." Advances and Applications in Statistics 92, no. 3 (2025): 449–70. https://doi.org/10.17654/0972361725020.

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In this article, a discretized form of Poisson-exponentiated Weibull distribution namely, discrete Poisson exponentiated Weibull (DPEW) distribution is introduced and studied. The model parameters are estimated using the method of maximum likelihood and its accuracy is established through simulated data. The adequacy of the new distribution in modelling count datasets, in comparison to alternative distributions, is demonstrated with different real datasets of asymmetric nature. A bivariate form of discrete Poisson-exponentiated Weibull distribution is also developed by considering Farlie-Gumbe

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Dohi, Tadashi, and Hiroyuki Okamura. "Failure-Correlated Opportunity-based Age Replacement Models." International Journal of Reliability, Quality and Safety Engineering 27, no. 02 (2019): 2040008. http://dx.doi.org/10.1142/s0218539320400082.

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In this paper, we extend the existing opportunity-based age replacement policies by taking account of dependency between the failure time and the arrival time of a replacement opportunity for one-unit system. Based on the bivariate probability distribution function of the failure time and the arrival time of the opportunity, we focus on two opportunity-based age replacement problems and characterize the cost-optimal age replacement policies which minimize the relevant expected costs, with the hazard gradient, which is a vector-valued bivariate hazard rate. Through numerical examples with the F

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Qura, Maha E., Aisha Fayomi, Mutua Kilai, and Ehab M. Almetwally. "Bivariate power Lomax distribution with medical applications." PLOS ONE 18, no. 3 (2023): e0282581. http://dx.doi.org/10.1371/journal.pone.0282581.

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In this paper, a bivariate power Lomax distribution based on Farlie-Gumbel-Morgenstern (FGM) copulas and univariate power Lomax distribution is proposed, which is referred to as BFGMPLx. It is a significant lifetime distribution for modeling bivariate lifetime data. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, product moments, positive quadrant dependence property, and Pearson’s correlation, have been studied. The reliability measures, such as the survival function, haz

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M. Salah, Mukhtar, M. El-Morshedy, M. S. Eliwa, and Haitham M. Yousof. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing." Mathematics 8, no. 11 (2020): 1949. http://dx.doi.org/10.3390/math8111949.

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The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method,

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ÜNÖZKAN, Hüseyin, and Mehmet YILMAZ. "A new transmutation: conditional copula with exponential distribution." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72, no. 2 (2023): 397–406. http://dx.doi.org/10.31801/cfsuasmas.1179189.

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In these days, many different techniques are implemented for generating distributions. The core aim in generating distribution, is better modeling capability. With generating new distribution more reliable and appropriate models are available for data sets. In this paper, a new distribution is gained by evaluating the conditional diagonal section of the bivariate Farlie-Gumbel-Morgenstern distribution with exponential marginals. Specifications and characteristics of this new distribution are studied. The statistical assessment and some reliability analyzes are carried out. The success of the n

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Jakaitienė, Audronė, and Danas Zuokas. "The survival regression model of competing risks for the family of Farlie–Gumbel–Morgenstern distributions." Lietuvos matematikos rinkinys 42 (December 20, 2002): 518–22. http://dx.doi.org/10.15388/lmr.2002.32987.

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In this paper the trivariate survival regression model for FGM family of distributions is constructed with marginal left-truncated logistic distributions. Two methods (using survival and hazard functions in the first case, and distributional density and ` `conditional'' survival function in the second case) are used when constructing likelihood function for model parameter estimation. Constructed survival model was run with the data of the ` `KRIS'' (The Kaunas Rotterdam Intervention Study), which lasted for 22 years from 1972. The results show, that using second case for likehhood function

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Mohamed, Mohamed. "A measure of inaccuracy in concomitants of ordered random variables under Farlie-Gumbel-Morgenstern family." Filomat 33, no. 15 (2019): 4931–42. http://dx.doi.org/10.2298/fil1915931m.

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In communication theory, for possible outcomes of an experiment, we have two basic problems for the statement of the experimenter: we may not have enough information (vague statement) or some of the information may be incorrect, which make inaccurate in either or both of these situations. In this article, a measure of inaccuracy and its residual between distributions of concomitants of generalized order statistics (1os) and parent random variable are extended. Results of inaccuracy for family distributions and stochastic comparisons are obtained. Furthermore, some properties of the proposed me

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Saminger-Platz, Susanne, Anna Kolesárová, Adam Šeliga, Radko Mesiar, and Erich Peter Klement. "New results on perturbation-based copulas." Dependence Modeling 9, no. 1 (2021): 347–73. http://dx.doi.org/10.1515/demo-2021-0116.

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Abstract A prominent example of a perturbation of the bivariate product copula (which characterizes stochastic independence) is the parametric family of Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some of them perturbing the product copula, while others perturb general copulas. A particularly interesting case is the perturbation of the product based on two functions in one variable where we highlight several special phenomena, e.g., extremal perturbed copulas. The constructions of the perturbations in t

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Barakat, H. M., M. A. Alawady, I. A. Husseiny, M. Nagy, A. H. Mansi, and M. O. Mohamed. "Bivariate Epanechnikov-exponential distribution: statistical properties, reliability measures, and applications to computer science data." AIMS Mathematics 9, no. 11 (2024): 32299–327. http://dx.doi.org/10.3934/math.20241550.

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<p>One important area of statistical theory and its applications to bivariate data modeling is the construction of families of bivariate distributions with specified marginals. This motivates the proposal of a bivariate distribution employing the Farlie-Gumbel-Morgenstern (FGM) copula and Epanechnikov exponential (EP-EX) marginal distribution, denoted by EP-EX-FGM. The EP-EX distribution is a complementing distribution, not a rival, to the exponential (EX) distribution. Its simple function shape and dependence on a single scale parameter make it an ideal choice for marginals in the sugge

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Ahmad, Hanan Haj, and Dina A. Ramadan. "Copula-Based Bivariate Modified Fréchet–Exponential Distributions: Construction, Properties, and Applications." Axioms 14, no. 6 (2025): 431. https://doi.org/10.3390/axioms14060431.

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The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding the flexible MEF margin in the FGM and AMH copulas. The resulting distributions accommodate a wide range of positive or negative dependence while retaining analytical traceability. Closed-form expressions for the joint and marginal de

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Patil, Dipak, U. V. Naik-Nimbalkar, and M. M. Kale. "Effect of Dependency on the Estimation of P[Y<X] in Exponential Stress-strength Models." Austrian Journal of Statistics 51, no. 4 (2022): 10–34. http://dx.doi.org/10.17713/ajs.v51i4.1293.

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We consider an expression for the probability R=P(Y<X) where the random variables X and Y denote strength and stress, respectively. Our aim is to study the effect of the dependency between X and Y on R. We assume that X and Y follow exponential distributions and their dependency is modeled by a copula with the dependency parameter theta. We obtain a closed-form expression for R for Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate exponential copulas and compute R for Gumbel-Hougaard (GH) copula using a Monte-Carlo integration technique. We plot a graph of R versus

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Chesneau, Christophe. "A study of the power-cosine copula." Open Journal of Mathematical Analysis 5, no. 1 (2021): 85–97. http://dx.doi.org/10.30538/psrp-oma2021.0086.

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Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of c

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Hamedani, G. G., Mustafa C. Korkmaz, Nadeem Shafique Butt, and Haitham M. Yousof. "The Type I Quasi Lambert Family." Pakistan Journal of Statistics and Operation Research, September 1, 2021, 545–58. http://dx.doi.org/10.18187/pjsor.v17i3.3562.

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A new G family of probability distributions called the type I quasi Lambert family is defined and applied for modeling real lifetime data. Some new bivariate type G families using "Farlie-Gumbel-Morgenstern copula", "modified Farlie-Gumbel-Morgenstern copula", "Clayton copula" and "Renyi's entropy copula" are derived. Three characterizations of the new family are presented. Some of its statistical properties are derived and studied. The maximum likelihood estimation, maximum product spacing estimation, least squares estimation, Anderson-Darling estimation and Cramer-von Mises estimation method

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Hamedani, G. G., Mustafa C. Korkmaz, Nadeem Shafique Butt, and Haitham M. Yousof. "The Type II Quasi Lambert Family." Pakistan Journal of Statistics and Operation Research, December 6, 2022, 963–83. http://dx.doi.org/10.18187/pjsor.v18i4.3907.

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Probability distributions and their families play an effective role in statistical modeling and statistical analysis. Recently, researchers have been increasingly interested in generating new families with high flexibility and low number of milestones. We propose and study a new family of continuous distributions. Relevant properties are presented. Many bivariate versions of the new family are derived under the Farlie-Gumbel-Morgenstern copula, modified Farlie-Gumbel-Morgenstern copula, Clayton copula, entropy copula and Ali-Mikhail-Haq copula. We present two characterizations of the new famil

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Aboraya, Mohamed. "Marshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling." Pakistan Journal of Statistics and Operation Research, June 3, 2021, 509–30. http://dx.doi.org/10.18187/pjsor.v17i2.3732.

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In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of m

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Barakat, H. M., M. A. Alawady, G. M. Mansour, and I. A. Husseiny. "Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants." Ricerche di Matematica, September 3, 2022. http://dx.doi.org/10.1007/s11587-022-00731-3.

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AbstractThe Sarmanov family of bivariate distributions is considered as the most flexible and efficient extended families of the traditional Farlie–Gumbel–Morgenstern family. The goal of this work is twofold. The first part focuses on revealing some novel aspects of the Sarmanov family’s dependency structure. In the second part, we study the Fisher information (FI) related to order statistics (OSs) and their concomitants about the shape-parameter of the Sarmanov family. The FI helps finding information contained in singly or multiply censored bivariate samples from the Sarmanov family. In addi

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Nagy, M., and Adel Fahad Alrasheedi. "Weighted extropy measures in general Morgenstern family under k-record values with application to medical data." AIP Advances 14, no. 1 (2024). http://dx.doi.org/10.1063/5.0188895.

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In this paper, we study the marginal distribution of concomitants of k-record (KR) values from generalized Farlie–Gumbel–Morgenstern (GFGM) of bivariate distributions. In addition, the joint distribution of concomitants of KR for this family is obtained. Furthermore, some useful recurrence relations between moments of concomitants are derived. In addition, the hazard rate, the reversed hazard rate, and mean residual life functions of concomitants for this family are obtained. Some recent new measures of information, such as weighted extropy, weighted cumulative past extropy, and weighted cumul

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Gómez-Déniz, Emilio, and Jorge V. Perez-Rodriguez. "Modelling dependence between daily tourist expenditure and length of stay." Tourism Economics, May 21, 2020, 135481662092519. http://dx.doi.org/10.1177/1354816620925192.

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In this article, tourists’ choice of the number of stays (length of stay, a discrete variable) and daily expenditure (a continuous variable) is modelled relaxing the linearity assumption and employing a structural form. A bivariate copula distribution, specified in terms of the marginal distributions of daily tourist expenditure and length of stay, is used to model and test dependence. We propose the Farlie–Gumbel–Morgenstern family of distributions, which provides a powerful tool to build a bivariate distribution with a flexible covariance structure and weak dependence. In addition, covariate

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Hashem, Atef F., M. A. Abdelkawy, Abdisalam Hassan Muse, and Haitham M. Yousof. "A novel generalized Weibull Poisson G class of continuous probabilistic distributions with some copulas, properties and applications to real-life datasets." Scientific Reports 14, no. 1 (2024). http://dx.doi.org/10.1038/s41598-023-49873-w.

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AbstractThe current study introduces and examines copula-coupled probability distributions. It explains their mathematical features and shows how they work with real datasets. Researchers, statisticians, and practitioners can use this study’s findings to build models that capture complex multivariate data interactions for informed decision-making. The versatility of compound G families of continuous probability models allows them to mimic a wide range of events. These incidents can range from system failure duration to transaction losses to annual accident rates. Due to their versatility, comp

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Folcher, Albert, and Jean‐François Quessy. "Semiparametric Copula‐Based Confidence Intervals on Level Curves for the Evaluation of the Risk Level Associated to Bivariate Events." Environmetrics 36, no. 2 (2025). https://doi.org/10.1002/env.70005.

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ABSTRACTIf is a random pair with distribution function , one can define the level curve of probability as the values of such that . This level curve is at the base of bivariate versions of return periods for the assessment of risk associated with extreme events. In most uses of bivariate return periods, the values taken by on this level curve are accorded equal significance. This paper adopts an innovative point‐of‐view by showing how to build confidence sets for the values of a pair of continuous random variables on a level curve. To this end, it is shown that the conditional distribution of

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Hui, Hsin Huang. "Forecasting Materials Demand from Multi-Source Ordering." July 2, 2017. https://doi.org/10.5281/zenodo.1131936.

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The downstream manufactures will order their materials from different upstream suppliers to maintain a certain level of the demand. This paper proposes a bivariate model to portray this phenomenon of material demand. We use empirical data to estimate the parameters of model and evaluate the RMSD of model calibration. The results show that the model has better fitness.

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Aliyu, Yakubu, and Umar Usman. "On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates." Journal of the Nigerian Society of Physical Sciences, May 1, 2023, 871. http://dx.doi.org/10.46481/jnsps.2023.871.

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An important alternative distribution to the Weibull, generalized exponen-tial and gamma distributions that is used in survival analysis is the Nadarajah-Haghighi exponential distribution. Similar to the Weibull, generalized exponen-tial and gamma distributions, the Nadarajah-Haghighi exponential distributionis an extension of the well known exponential distribution. In this paper, a copulafunction commonly used to model very weak linear dependence was used to intro-duced a bivariate Nadarajah-Haghighi distribution. The joint survival function,joint probability density function and joint cumul

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SUSAM, Selim Orhun. "A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial." Hacettepe Journal of Mathematics and Statistics, December 31, 2022, 1–14. http://dx.doi.org/10.15672/hujms.993698.

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"Inference for Stress-Strength Models Based on the Bivariate General Farlie-Gumbel-Morgenstern Distributions." Journal of Statistics Applications & Probability Letters 7, no. 3 (2020): 141–50. http://dx.doi.org/10.18576/jsapl/070304.

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Muhammed, Hiba Zeyada, and Hagar Mohamed Abdelghany. "Modified Weighted Uniform Distribution And Its Bivariate Extension." Journal of Probability and Statistical Science 21, no. 1 (2023). http://dx.doi.org/10.37119/jpss2023.v21i1.637.

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In this paper a new version of weighted uniform distribution is constructed and studied. The statistical properties of the new distribution including the behavior of hazard and reversed hazard functions, moments, the central moments, moment generating function, mean, variance, coefficient of skewness, coefficient of kurtosis, median, mode, quantile , stochastic ordering and order statistics are also obtained, a simulation study and real data applications are performed. Moreover, a bivariate extension of the new distribution named the bivariate modified uniform (BMWU) distribution is introduced

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Muhammed, Hiba Zeyada, and Hagar Mohamed Abdelghany. "Modified Weighted Rayleigh Distribution and Its Bivariate Extension." Journal of Probability and Statistical Science 21, no. 1 (2023). http://dx.doi.org/10.37119/jpss2023.v21i1.640.

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In this paper, a new version of weighted Rayleigh distribution is constructed and studied. The statistical properties of the new distribution including the behavior of hazard and reversed hazard functions, moments, the central moments, moment generating function, mean, variance, coefficient of skewness, coefficient of kurtosis, median, mode, quantiles, stochastic ordering, exact information matrix and order statistics are also obtained, a simulation study and real data applications are performed. Furthermore, a bivariate extension of the new distribution called the bivariate modified Rayleigh

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Elgawad, Mohamed A. Abd, Haroon M. Barakat, and Metwally A. Alawady. "Concomitants of Generalized Order Statistics Under the Generalization of Farlie–Gumbel–Morgenstern- Type Bivariate Distributions." Bulletin of the Iranian Mathematical Society, July 4, 2020. http://dx.doi.org/10.1007/s41980-020-00427-0.

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Hamed, Mohamed S., Gauss M. Cordeiro, and Haitham M. Yousof. "A New Compound Lomax Model: Properties, Copulas, Modeling and Risk Analysis Utilizing the Negatively Skewed Insurance Claims Data." Pakistan Journal of Statistics and Operation Research, September 9, 2022, 601–31. http://dx.doi.org/10.18187/pjsor.v18i3.3652.

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Analyzing the future values of anticipated claims is essential in order for insurance companies to avoid major losses caused by prospective future claims. This study proposes a novel three-parameter compound Lomax extension. The new density can be "monotonically declining", "symmetric", "bimodal-asymmetric", "asymmetric with right tail", "asymmetric with wide peak" or "asymmetric with left tail". The new hazard rate can take the following shapes: "J-shape", "bathtub (U-shape)", "upside down-increasing", "decreasing-constant", and "upside down-increasing". We use some common copulas, including

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