On Concomitants of Dual Generalized Order Statistics for a Bivariate Inverse Exponential Distribution

Shahbaz, Saman Hanif; Shahbaz, Muhammad

doi:10.29020/nybg.ejpam.v11i4.3257

Cited by 4 publications

(4 citation statements)

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“…where v(x) ∈ [−0.5, 1]. Following the idea of Shahbaz [10] and by the definition of the conditional probability, the joint probability distribution function of X and Y is given by…”

Section: The Bivariate Extended Standard U-quadratic Distributionmentioning

confidence: 99%

“…Let K 2 be another random variable such that the conditional distribution of K 2 given K 1 follows a Km distribution with parameters h(k 1 ) > 0 and b > 0. From the work of Shahbaz et al [10], the joint pdf of K 1 and K 2 is given by…”

Section: Applicationmentioning

confidence: 99%

“…In particular, they derived the pseudo-Weibull and pseudo-gamma distributions as the linear combinations of the Weibull and gamma random variables, respectively. Shahbaz et al [10] formed a bivariate exponential distribution as the compound distribution of two exponential random variables. Aside from the bivariate exponential distribution, many derived bivariate distributions were formulated using this idea such as the bivariate pseudo-Weibull distribution [9], bivariate pseudo-Rayleigh distribution [7], bivariate pseudo-inverse Rayleigh distribution [5], bivariate pseudo-Gumbel distribution [8], bivariate inverse exponential distribution [11], among others.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we will follow the idea of Shahbaz et al [10] to expand the extended Standard U-quadratic distribution into a bivariate case. We will also derive some properties of the proposed distribution such as the marginal distribution, conditional distribution, conditional moments, product and ratio moments, Pearson correlation coefficient, joint moment generating function, and the stress -strength parameter.…”

Section: Introductionmentioning

confidence: 99%

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On the Bivariate Extension of the Extended Standard U-quadratic Distribution

Lakibul,

Polestico,

Supe

2024

Eur. J. Pure Appl. Math.

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This paper derives the bivariate version of the extended standard U-quadratic (eSU) distribution using the method of compounding or pseudo family of distributions. The joint probability and cumulative distribution functions of the derived distribution are obtained and it is observed that the said distribution can generate bivariate shape with the following properties: $(i)$ $X$ and $Y$ have bathtub shapes; $(ii)$ $X$ has constant and $Y$ has bathtub shapes; and $(iii)$ $X$ has inverted bathtub and $Y$ has bathtub shapes. Moreover, some properties of the derived distribution such as the marginal distribution, conditional distributions, conditional moments, product and ratio moments are derived. Further, the maximum likelihood estimation is performed to estimate the parameters of the derived distribution. Also, a simulation study is carried out to evaluate the behavior of the estimates of the parameters. Moreover, we derive a new bivariate Kumaraswamy distribution and use it to simulate bivariate data with $X$ and $Y$ having bathtub shapes. Furthermore, A new bivariate version of the Cubic Transmuted Uniform (CTU) distribution is also derived. Finally, the proposed Bivariate eSU distribution is applied to simulated data and compared with the said Bivarite Cubic Transmuted Uniform distribution. The result shows that the proposed Bivariate eSU distribution provides a better fit for the said simulated dataset as compared with the Bivariate CTU distribution.

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“…where v(x) ∈ [−0.5, 1]. Following the idea of Shahbaz [10] and by the definition of the conditional probability, the joint probability distribution function of X and Y is given by…”

Section: The Bivariate Extended Standard U-quadratic Distributionmentioning

confidence: 99%

Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Bivariate Extension of the Extended Standard U-quadratic Distribution

Lakibul,

Polestico,

Supe

2024

Eur. J. Pure Appl. Math.

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Concomitants of Generalized Order Statistics from Huang–Kotz Farlie–Gumble–Morgenstern Bivariate Distribution: Some Information Measures

Elgawad

Alawady

Barakat

et al. 2019

Bull. Malays. Math. Sci. Soc.

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On concomitants of dual generalized order statistics from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions

Alawady

Barakat

Xiong

et al. 2021

Asian-European J. Math.

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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 concomitants are obtained. Moreover, most of the paper results are extended to any arbitrary distribution. Finally, an application of these results is given for bivariate generalized exponential distribution.

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On Concomitants of Dual Generalized Order Statistics for a Bivariate Inverse Exponential Distribution

Cited by 4 publications

References 10 publications

On the Bivariate Extension of the Extended Standard U-quadratic Distribution

On the Bivariate Extension of the Extended Standard U-quadratic Distribution

Concomitants of Generalized Order Statistics from Huang–Kotz Farlie–Gumble–Morgenstern Bivariate Distribution: Some Information Measures

On concomitants of dual generalized order statistics from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions

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