Concomitants of Ordered Variables from Huang–Kotz FGM Type Bivariate Generalized Exponential Distribution

Barakat, H. M.; Nigm, E. M.; Syam, A. H.

doi:10.1007/s40840-017-0489-5

Cited by 22 publications

(12 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, Table 1 shows that the values of max are irregularly fluctuated with changing the values of the parameters p and m. However the maximum value of max , which is 0.4214, reaches at m = 25 and p = 4.5. This maximum value is a significant improvement comparing with the upper bound "0.2921"obtained by [7] for the model MTBGED and is also a satisfactory improvement comparing with the upper pound "0.3937"obtained by [8] for the model HK-FGMGE. This fact gives a satisfactory motivation to deal with GFGM-GE rather than MTBGED and HK-FGMGE.…”

supporting

confidence: 59%

“…In the last two decades much attention has been paid to the concomitants of order statistics models, see, e.g. [7,8,13,14]. The importance of these models increased owing to the rigorous demand of natural science, social science and economics to study the problems which generally depend on two different dependent characteristics.…”

Section: Concomitants Of Order Statistics Based On Gfgm-gementioning

confidence: 99%

“…Moreover, they obtained some recurrence relations between moments of concomitants of order statistics. Recently, [8] extended all the results of [7] to HK-FGM family for bivariate-GE distribution (denoted by HK-FGMGE). Moreover, some new results, which were not be obtained by [7], for FGM family, were given.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, some new results, which were not be obtained by [7], for FGM family, were given. Finally, [8] studied the asymptotic behavior of the concomitants of order statistics and made some corrections of [7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Concomitants of Order Statistics and Record Values from Generalization of FGM Bivariate-Generalized Exponential Distribution

Barakat¹,

Nigm²,

Alawady³

et al. 2019

JSTA

View full text Add to dashboard Cite

A B S T R A C TWe introduce the generalized Farlie Gumbel Morgenstern (FGM) type bivariate-generalized 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.

show abstract

supporting

confidence: 59%

Section: Concomitants Of Order Statistics Based On Gfgm-gementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Concomitants of Order Statistics and Record Values from Generalization of FGM Bivariate-Generalized Exponential Distribution

Barakat¹,

Nigm²,

Alawady³

et al. 2019

JSTA

View full text Add to dashboard Cite

show abstract

“…For example, the FI number defined by (15) seems to be wrong, because we have −1 ≤ αC (r, n, m, k) ≤ 1, which implies that log(−1 + αC (r, n, m, k)) and log(−1 − αC (r, n, m, k)) have no meaning, since −2 ≤ −1 + αC (r, n, m, k) ≤ 0 and −2 ≤ −1 − αC (r, n, m, k) ≤ 0. Moreover, the integration defined in (19) seems to be wrong.…”

Section: Remarkmentioning

confidence: 99%

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

Elgawad

Barakat

Xiong

et al. 2021

Entropy

View full text Add to dashboard Cite

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,⋯,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

show abstract

Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants

et al. 2022

Self Cite

View full text Add to dashboard Cite

The 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 addition, the FI about the mean and shape parameter of exponential and power distributions in concomitants of OSs is evaluated, respectively. Finally, the cumulative residual FI in the concomitants of OSs based on the Sarmanov family is derived.

show abstract

Concomitants of Ordered Variables from Huang–Kotz FGM Type Bivariate Generalized Exponential Distribution

Cited by 22 publications

References 16 publications

Concomitants of Order Statistics and Record Values from Generalization of FGM Bivariate-Generalized Exponential Distribution

Concomitants of Order Statistics and Record Values from Generalization of FGM Bivariate-Generalized Exponential Distribution

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants

Contact Info

Product

Resources

About